Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Elementary Algebra
In the following exercises, solve each coin word problem. 166. Joe’s wallet contains $1 and $5 bills worth $47. The number of $1 bills is five more than the number of $5 bills. How many of each bill does he have?In the following exercises, solve each coin word problem. 167. Rachelle has $6.30 in nickels and quarters in her coin purse. The number of nickels is twice the number of quarters. How many coins of each type does she have?In the following exercises, solve each coin word problem. 168. Deloise has $1.20 in pennies and nickels in a jar on her desk. The number of pennies is three times the number of nickels. How many coins of each type does she have?In the following exercises, solve each coin word problem. 169. Harrison has $9.30 in his coin collection, all in pennies and dimes. The number of dimes is three times the number of pennies. How many coins of each type does he have?In the following exercises, solve each coin word problem. 170. Ivan has $8.75 in nickels and quarters in his desk drawer. The number of nickels is twice the number of quarters. How many coins of each type does he have?In the following exercises, solve each coin word problem. 171. In a cash drawer there is $125 in $5 and $10 bills. The number of $10 bills is twice the number of $5 bills. How many of each are in the drawer?In the following exercises, solve each coin word problem. 172. John has $175 in $5 and $10 bills in his drawer. The number of $5 bills is three times the number of $10 bills. How many of each are in the drawer?In the following exercises, solve each coin word problem. 173. Carolyn has $2.55 in her purse in nickels and dimes. The number of nickels is nine less than three times the number of dimes. Find the number of each type of coin.In the following exercises, solve each coin word problem. 174. Julio has $2.75 in his pocket in nickels and dimes. The number of dimes is 10 less than twice the number of nickels. Find the number of each type of coin.In the following exercises, solve each coin word problem. 175. Chi has $11.30 in dimes and quarters. The number of dimes is three more than three times the number of quarters. How many of each are there?In the following exercises, solve each coin word problem. 176. Tyler has $9.70 in dimes and quarters. The number of quarters is eight more than four times the number of dimes. How many of each coin does he have?In the following exercises, solve each coin word problem. 177. Mukul has $3.75 in quarters, dimes and nickels in his pocket. He has five more dimes than quarters and nine more nickels than quarters. How many of each coin are in his pocket?In the following exercises, solve each coin word problem. 178. Vina has $4.70 in quarters, dimes and nickels in her purse. She has eight more dimes than quarters and six more nickels than quarters. How many of each coin are in her purse?In the following exercises, solve each ticket or stamp word problem. 179. The school play sold $550 in tickets one night. The number of $8 adult tickets was 10 less than twice the number of $5 child tickets. How many of each ticket were sold?In the following exercises, solve each ticket or stamp word problem. 180. If the number of $8 child tickets is seventeen less than three times the number of $12 adult tickets and the theater took in $584, how many of each ticket were sold?In the following exercises, solve each ticket or stamp word problem. 181. The movie theater took in $1,220 one Monday night. The number of $7 child tickets was ten more than twice the number of $9 adult tickets. How many of each were sold?In the following exercises, solve each ticket or stamp word problem. 182. The ball game sold $1,340 in tickets one Saturday. The number of $12 adult tickets was 15 more than twice the number of $5 child tickets. How many of each were sold?In the following exercises, solve each ticket or stamp word problem. 183. The ice rink sold 95 tickets for the afternoon skating session, for a total of $828. General admission tickets cost $10 each and youth tickets cost $8 each. How many general admission tickets and how many youth tickets were sold?In the following exercises, solve each ticket or stamp word problem. 184. For the 7:30 show time, 140 movie tickets were sold. Receipts from the $13 adult tickets and the $10 senior tickets totaled $1,664. How many adult tickets and how many senior tickets were sold?In the following exercises, solve each ticket or stamp word problem. 185. The box office sold 360 tickets to a concert at the college. The total receipts were $4170. General admission tickets cost $15 and student tickets cost $10. How many of each kind of ticket was sold?In the following exercises, solve each ticket or stamp word problem. 186. Last Saturday, the museum box office sold 281 tickets for a total of $3954. Adult tickets cost $15 and student tickets cost $12. How many of each kind of ticket was sold?In the following exercises, solve each ticket or stamp word problem. 187. Julie went to the post office and bought both $0.41 stamps and $0.26 postcards. She spent $51.40. The number of stamps was 20 more than twice the number of postcards. How many of each did she buy?In the following exercises, solve each ticket or stamp word problem. 188. Jason went to the post office and bought both $0.41 stamps and $0.26 postcards and spent $10.28. The number of stamps was four more than twice the number of postcards. How many of each did he buy?In the following exercises, solve each ticket or stamp word problem. 189. Maria spent $12.50 at the post office. She bought three times as many $0.41 stamps as $0.02 stamps. How many of each did she buy?In the following exercises, solve each ticket or stamp word problem. 190. Hector spent $33.20 at the post office. He bought four times as many $0.41 stamps as $0.02 stamps. How many of each did he buy?In the following exercises, solve each ticket or stamp word problem. 191. Hilda has $210 worth of $10 and $12 stock shares. The numbers of $10 shares is five more than twice the number of $12 shares. How many of each does she have?In the following exercises, solve each ticket or stamp word problem. 192. Mario invested $475 in $45 and $25 stock shares. The number of $25 shares was five less than three times the number of $45 shares. How many of each type of share did he buy?In the following exercises, solve each mixture word problem. 193. Lauren in making 15 liters of mimosas for a brunch banquet. Orange juice costs her $1.50 per liter and champagne costs her $12 per liter. How many liters of orange juice and how many liters of champagne should she use for the mimosas to cost Lauren $5 per liter?In the following exercises, solve each mixture word problem. 194. Macario is making 12 pounds of nut mixture with macadamia nuts and almonds. Macadamia nuts cost $9 per pound and almonds cost $5.25 per pound. How many pounds of macadamia nuts and how many pounds of almonds should Macario use for the mixture to cost $6.50 perpound to make?In the following exercises, solve each mixture word problem. 195. Kaapo is mixing Kona beans and Maui beans to make 25 pounds of coffee blend. Kona beans cost Kaapo $15 per pound and Maui beans cost $24 per pound. How many pounds of each coffee bean should Kaapo use for his blend to cost him $17.70 per pound?In the following exercises, solve each mixture word problem. 196. Estelle is making 30 pounds of fruit salad from strawberries and blueberries. Strawberries cost $1.80 per pound and blueberries cost $4.50 per pound. If Estelle wants the fruit salad to cost her $2.52 per pound, how many pounds of each berry should she use?In the following exercises, solve each mixture word problem. 197. Carmen wants to tile the floor of his house. He will need 1000 square feet of tile. He will do most of the floor with a tile that costs $1.50 per square foot, but also wants to use an accent tile that costs $9.00 per square foot. How many square feet of each tile should he plan to use if he wants the overall cost to be $3 per square foot?In the following exercises, solve each mixture word problem. 198. Riley is planning to plant a lawn in his yard. He will need nine pounds of grass seed. He wants to mix Bermuda seed that costs $4.80 per pound with Fescue seed that costs $3.50 per pound. How much of each seed should he buy so that the overall cost will be $4.02 per pound?In the following exercises, solve each mixture word problem. 199. Vartan was paid $25,000 for a cell phone app that he wrote and wants to invest it to save for his son’s education. He wants to put some of the money into a bond that pays 4% annual interest and the rest into stocks that pay 9% annual interest. If he wants to earn 7.4% annual interest on the total amount, how much money should he invest in each account?In the following exercises, solve each mixture word problem. 200. Vern sold his 1964 Ford Mustang for $55,000 and wants to invest the money to earn him 5.8% interest per year. He will put some of the money into Fund A that earns 3% per year and the rest in Fund B that earns 10% per year. How much should he invest into each fund if he wants to earn 5.8% interest per year on the total amount?In the following exercises, solve each mixture word problem. 201. Stephanie inherited $40,000. She wants to put some of the money in a certificate of deposit that pays 2.1% interest per year and the rest in a mutual fund account that pays 6.5% per year. How much should she invest in each account if she wants to earn 5.4% interest per year on the total amount?In the following exercises, solve each mixture word problem. 202. Avery and Caden have saved $27,000 towards a down payment on a house. They want to keep some of the money in a bank account that pays 2.4% annual interest and the rest in a stock fund that pays 7.2% annual interest. How much should they put into each account so that they earn 6% interest per year?In the following exercises, solve each mixture word problem. 203. Dominic pays 7% interest on his $15,000 college loan and 12% interest on his $11,000 car loan. What average interest rate does he pay on the total $26,000 he owes? (Round your answer to the nearest tenth of a percent.)In the following exercises, solve each mixture word problem. 204. Liam borrowed a total of $35,000 to pay for college. He pays his parents 3% interest on the $8,000 he borrowed from them and pays the bank 6.8% on the rest. What average interest rate does he pay on the total $35,000? (Round your answer to the nearest tenth of a percent.)As the treasurer of her daughter’s Girl Scout troop, Laney collected money for some girls and adults to go to a 3-day camp. Each girl paid $75 and each adult paid $30. The total amount of money collected for camp was $765. If the number of girls is three times the number of adults, how many girls and how many adults paid for camp?Laurie was completing the treasurer’s report for her son’s Boy Scout troop at the end of the school year. She didn’t remember how many boys had paid the $15 full-year registration fee and how many had paid the $10 partial-year fee. She knew that the number of boys who paid for a full-year was ten more than the number who paid for a partial-year. If $250 was collected for all the registrations, how many boys had paid the full-year fee and how many had paid the partial-year fee?Suppose you have six quarters, nine dimes, and four pennies. Explain how you find the total value of all the coins.Do you find it helpful to use a table when solving coin problems? Why or why not?In the table used to solve coin problems, one column is labeled “number” and another column is labeled “value.” What is the difference between the “number” and the “value?”What similarities and differences did you see between solving the coin problems and the ticket and stamp problems?The measures of two angles of a triangle are 31 and 128 degrees. Find the measure of the third angle.The measures of two angles of a triangle are 49 and 75 degrees. Find the measure of the third angle.The perimeter of a triangular garden is 48 feet. The lengths of two sides are 18 feet and 22 feet. How long is the third side?The lengths of two sides of a triangular window are seven feet and five feet. The perimeter is 18 feet. How long is the third side?The area of a triangular painting is 126 square inches. The base is 18 inches. What is the height?A triangular tent door has area 15 square feet. The height is five feet. What is the base?One angle of a right triangle measures 56°. What is the measure of the other small angle?One angle of a right triangle measures 45°. What is the measure of the other small angle?The measure of one angle of a right triangle is 50° more than the measure of the smallest angle. Find the measures of all three angles.The measure of one angle of a right triangle is 30° more than the measure of the smallest angle. Find the measures of all three angles.Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle shown below.Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle shown below.Use the Pythagorean Theorem to find the length of the leg in the triangle shown below.Use the Pythagorean Theorem to find the length of the leg in the triangle shown below.John puts the base of a 13-foot ladder five feet from the wall of his house as shown below. How far up the wall does the ladder reach?Randy wants to attach a 17 foot string of lights to the top of the 15 foot mast of his sailboat, as shown below. How far from the base of the mast should he attach the end of the light string?The length of a rectangle is 120 yards and the width is 50 yards. What is the perimeter?The length of a rectangle is 62 feet and the width is 48 feet. What is the perimeter?The area of a rectangle is 598 square feet. The length is 23 feet. What is the width?The width of a rectangle is 21 meters. The area is 609 square meters. What is the length?Find the length of a rectangle with: perimeter 80 and width 25.Find the length of a rectangle with: perimeter 30 and width 6.The width of a rectangle is seven meters less than the length. The perimeter is 58 meters. Find the length and width.The length of a rectangle is eight feet more than the width. The perimeter is 60 feet. Find the length and width.The length of a rectangle is eight more than twice the width. The perimeter is 64. Find the length and width.The width of a rectangle is six less than twice the length. The perimeter is 18. Find the length and width.The perimeter of a rectangular swimming pool is 200 feet. The length is 40 feet more than the width. Find the length and width.The length of a rectangular garden is 30 yards more than the width. The perimeter is 300 yards. Find the length and width.In the following exercises, solve using triangle properties. 211. The measures of two angles of a triangle are 26 and 98 degrees. Find the measure of the third angle.In the following exercises, solve using triangle properties. 212. The measures of two angles of a triangle are 61 and 84 degrees. Find the measure of the third angle.In the following exercises, solve using triangle properties. 213. The measures of two angles of a triangle are 105 and 31 degrees. Find the measure of the third angle.In the following exercises, solve using triangle properties. 214. The measures of two angles of a triangle are 47 and 72 degrees. Find the measure of the third angle.In the following exercises, solve using triangle properties. 215. The perimeter of a triangular pool is 36 yards. The lengths of two sides are 10 yards and 15 yards. How long is the third side?In the following exercises, solve using triangle properties. 216. A triangular courtyard has perimeter 120 meters. The lengths of two sides are 30 meters and 50 meters. How long is the third side?In the following exercises, solve using triangle properties. 217. If a triangle has sides 6 feet and 9 feet and the perimeter is 23 feet, how long is the third side?In the following exercises, solve using triangle properties. 218. If a triangle has sides 14 centimeters and 18 centimeters and the perimeter is 49 centimeters, how long is the third side?In the following exercises, solve using triangle properties. 219. A triangular flag has base one foot and height 1.5 foot. What is its area?In the following exercises, solve using triangle properties. 220. A triangular window has base eight feet and height six feet. What is its area?In the following exercises, solve using triangle properties. 221. What is the base of a triangle with area 207 square inches and height 18 inches?In the following exercises, solve using triangle properties. 222. What is the height of a triangle with area 893 square inches and base 38 inches?In the following exercises, solve using triangle properties. 223. One angle of a right triangle measures 33 degrees. What is the measure of the other small angle?In the following exercises, solve using triangle properties. 224. One angle of a right triangle measures 51 degrees. What is the measure of the other small angle?In the following exercises, solve using triangle properties. 225. One angle of a right triangle measures 22.5 degrees. What is the measure of the other small angle?In the following exercises, solve using triangle properties. 226. One angle of a right triangle measures 36.5 degrees. What is the measure of the other small angle?In the following exercises, solve using triangle properties. 227. The perimeter of a triangle is 39 feet. One side of the triangle is one foot longer than the second side. The third side is two feet longer than the second side. Find the length of each side.In the following exercises, solve using triangle properties. 228. The perimeter of a triangle is 35 feet. One side of the triangle is five feet longer than the second side. The third side is three feet longer than the second side. Find the length of each side.In the following exercises, solve using triangle properties. 229. One side of a triangle is twice the shortest side. The third side is five feet more than the shortest side. The perimeter is 17 feet. Find the lengths of all three sides.In the following exercises, solve using triangle properties. 230. One side of a triangle is three times the shortest side. The third side is three feet more than the shortest side. The perimeter is 13 feet. Find the lengths of all three sides.In the following exercises, solve using triangle properties. 231. The two smaller angles of a right triangle have equal measures. Find the measures of all three angles.In the following exercises, solve using triangle properties. 232. The measure of the smallest angle of a right triangle is 20° less than the measure of the next larger angle. Find the measures of all three angles.In the following exercises, solve using triangle properties. 233. The angles in a triangle are such that one angle is twice the smallest angle, while the third angle is three times as large as the smallest angle. Find the measures of all three angles.In the following exercises, solve using triangle properties. 234. The angles in a triangle are such that one angle is 20° more than the smallest angle, while the third angle is three times as large as the smallest angle. Find the measures of all three angles.In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse. 235.In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse. 236.In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse. 237.In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse. 238.In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth, if necessary. 239.In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth, if necessary. 240.In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth, if necessary. 241.In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth, if necessary. 242.In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth, if necessary. 243.In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth, if necessary. 244.In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth, if necessary. 245.In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth, if necessary. 246.In the following exercises, solve using the Pythagorean Theorem. Approximate to the nearest tenth, if necessary. 247. A 13-foot string of lights will be attached to the top of a 12-foot pole for a holiday display, as shown below. How far from the base of the pole should the end of the string of lights be anchored?In the following exercises, solve using the Pythagorean Theorem. Approximate to the nearest tenth, if necessary. 248. Pam wants to put a banner across her garage door, as shown below, to congratulate her son for his college graduation. The garage door is 12 feet high and 16 feet wide. How long should the banner be to fit the garage door?In the following exercises, solve using the Pythagorean Theorem. Approximate to the nearest tenth, if necessary. 249. Chi is planning to put a path of paving stones through her flower garden, as shown below. The flower garden is a square with side 10 feet. What will the length of the path be?In the following exercises, solve using the Pythagorean Theorem. Approximate to the nearest tenth, if necessary. 250. Brian borrowed a 20 foot extension ladder to usewhen he paints his house. If he sets the base of theladder 6 feet from the house, as shown below, how far up will the top of the ladder reach?In the following exercises, solve using rectangle properties. 251. The length of a rectangle is 85 feet and the width is 45 feet. What is the perimeter?In the following exercises, solve using rectangle properties. 252. The length of a rectangle is 26 inches and the width is 58 inches. What is the perimeter?In the following exercises, solve using rectangle properties. 253. A rectangular room is 15 feet wide by 14 feet long. What is its perimeter?In the following exercises, solve using rectangle properties. 254. A driveway is in the shape of a rectangle 20 feet wide by 35 feet long. What is its perimeter?In the following exercises, solve using rectangle properties. 255. The area of a rectangle is 414 square meters. The length is 18 meters. What is the width?In the following exercises, solve using rectangle properties. 256. The area of a rectangle is 782 square centimeters. The width is 17 centimeters. What is the length?In the following exercises, solve using rectangle properties. 257. The width of a rectangular window is 24 inches. The area is 624 square inches. What is the length?In the following exercises, solve using rectangle properties. 258. The length of a rectangular poster is 28 inches. The area is 1316 square inches. What is the width?In the following exercises, solve using rectangle properties. 259. Find the length of a rectangle with perimeter 124 and width 38.In the following exercises, solve using rectangle properties. 260. Find the width of a rectangle with perimeter 92 and length 19.In the following exercises, solve using rectangle properties. 261. Find the width of a rectangle with perimeter 16.2 and length 3.2.In the following exercises, solve using rectangle properties. 262. Find the length of a rectangle with perimeter 20.2 and width 7.8.In the following exercises, solve using rectangle properties. 263. The length of a rectangle is nine inches more than the width. The perimeter is 46 inches. Find the length and the width.In the following exercises, solve using rectangle properties. 264. The width of a rectangle is eight inches more than the length. The perimeter is 52 inches. Find the length and the width.In the following exercises, solve using rectangle properties. 265. The perimeter of a rectangle is 58 meters. The width of the rectangle is five meters less than the length. Find the length and the width of the rectangle.In the following exercises, solve using rectangle properties. 266. The perimeter of a rectangle is 62 feet. The width is seven feet less than the length. Find the length and the width.In the following exercises, solve using rectangle properties. 267. The width of the rectangle is 0.7 meters less than the length. The perimeter of a rectangle is 52.6 meters. Find the dimensions of the rectangle.In the following exercises, solve using rectangle properties. 268. The length of the rectangle is 1.1 meters less than the width. The perimeter of a rectangle is 49.4 meters. Find the dimensions of the rectangle.In the following exercises, solve using rectangle properties. 269. The perimeter of a rectangle is 150 feet. The length of the rectangle is twice the width. Find the length and width of the rectangle.In the following exercises, solve using rectangle properties. 270. The length of a rectangle is three times the width. The perimeter of the rectangle is 72 feet. Find the length and width of the rectangle.In the following exercises, solve using rectangle properties. 271. The length of a rectangle is three meters less than twice the width. The perimeter of the rectangle is 36 meters. Find the dimensions of the rectangle.In the following exercises, solve using rectangle properties. 272. The length of a rectangle is five inches more than twice the width. The perimeter is 34 inches. Find the length and width.In the following exercises, solve using rectangle properties. 273. The perimeter of a rectangular field is 560 yards. The length is 40 yards more than the width. Find the length and width of the field.In the following exercises, solve using rectangle properties. 274. The perimeter of a rectangular atrium is 160 feet. The length is 16 feet more than the width. Find the length and width of the atrium.In the following exercises, solve using rectangle properties. 275. A rectangular parking lot has perimeter 250 feet. The length is five feet more than twice the width. Find the length and width of the parking lot.In the following exercises, solve using rectangle properties. 276. A rectangular rug has perimeter 240 inches. The length is 12 inches more than twice the width. Find the length and width of the rug.Christa wants to put a fence around her triangular flowerbed. The sides of the flowerbed are six feet, eight feet and 10 feet. How many feet of fencing will she need to enclose her flowerbed?Jose just removed the children’s playset from his back yard to make room for a rectangular garden. He wants to put a fence around the garden to keep out the dog. He has a 50 foot roll of fence in his garage that he plans to use. To fit in the backyard, the width of the garden must be 10 feet. How long can he make the other length?If you need to put tile on your kitchen floor, do you need to know the perimeter or the area of the kitchen? Explain your reasoning.If you need to put a fence around your backyard, do you need to know the perimeter or the area of the backyard? Explain your reasoning.Look at the two figures below. (a) Which figure looks like it has the larger area? (b) Which looks like it has the larger perimeter? (c) Now calculate the area and perimeter of each figure. (d) Which has the larger area? (e) Which has the larger perimeter?Write a geometry word problem that relates toyour life experience, then solve it and explain all your steps.Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.Jeromy can drive from his house in Cleveland to his college in Chicago in 4.5 hours. It takes his mother 6 hours to make the same drive. Jeromy drives 20 miles per hour faster than his mother. Find Jeromy’s speed and his mother’s speed.Carina is driving from her home in Anaheim to Berkeley on the same day her brother is driving from Berkeley to Anaheim, so they decide to meet for lunch along the way in Buttonwillow. The distance from Anaheim to Berkeley is 410 miles. It takes Carina 3 hours to get to Buttonwillow, while her brother drives 4 hours to get there. The average speed Carina’s brother drove was 15 miles per hour faster than Carina’s average speed. Find Carina’s and her brother’s average speeds.Ashley goes to college in Minneapolis, 234 miles from her home in Sioux Falls. She wants her parents to bring her more winter clothes, so they decide to meet at a restaurant on the road between Minneapolis and Sioux Falls. Ashley and her parents both drove 2 hours to the restaurant. Ashley’s average speed was seven miles per hour faster than her parents’ average speed. Find Ashley’s and her parents’ average speed.Pierre and Monique leave their home in Portland at the same time. Pierre drives north on the turnpike at a speed of 75 miles per hour while Monique drives south at a speed of 68 miles per hour. How long will it take them to be 429 miles apart?Thanh and Nhat leave their office in Sacramento at the same time. Thanh drives north on I-5 at a speed of 72 miles per hour. Nhat drives south on I-5 at a speed of 76 miles per hour. How long will it take them to be 330 miles apart?Suzy takes 50 minutes to hike uphill from the parking lot to the lookout tower. It takes her 30 minutes to hike back down to the parking lot. Her speed going downhill is 1.2 miles per hour faster than her speed going uphill. Find Suzy’s uphill and downhill speeds.Llewyn takes 45 minutes to drive his boat upstream from the dock to his favorite fishing spot. It takes him 30 minutes to drive the boat back downstream to the dock. The boat’s speed going downstream is four miles per hour faster than its speed going upstream. Find the boat’s upstream and downstream speeds.Cruz is training to compete in a triathlon. He left his house at 6:00 and ran until 7:30. Then he rode his bike until 9:45. He covered a total distance of 51 miles. His speed when biking was 1.6 times his speed when running. Find Cruz’s biking and running speeds.Phuong left home on his bicycle at 10:00. He rode on the flat street until 11:15, then rode uphill until 11:45. He rode a total of 31 miles. His speed riding uphill was 0.6 times his speed on the flat street. Find his speed biking uphill and on the flat street.In the following exercises, solve. 283. Lilah is moving from Portland to Seattle. It takes her three hours to go by train. Mason leaves the train station in Portland and drives to the train station in Seattle with all Lilah’s boxes in his car. It takes him 2.4 hours to get to Seattle, driving at 15 miles per hour faster than the speed of the train. Find Mason’s speed and the speed of the train.In the following exercises, solve. 284. Kathy and Cheryl are walking in a fundraiser. Kathy completes the course in 4.8 hours and Cheryl completes the course in 8 hours. Kathy walks two miles per hour faster than Cheryl. Find Kathy’sspeed and Cheryl’s speed.In the following exercises, solve. 285. Two busses go from Sacramento for San Diego. The express bus makes the trip in 6.8 hours and the local bus takes 10.2 hours for the trip. The speed of the express bus is 25 mph faster than the speed of the local bus. Find the speed of both busses.In the following exercises, solve. 286. A commercial jet and a private airplane fly from Denver to Phoenix. It takes the commercial jet 1.1 hours for the flight, and it takes the private airplane 1.8 hours. The speed of the commercial jet is 210 miles per hour faster than the speed of the private airplane. Find the speed of both airplanes.In the following exercises, solve. 287. Saul drove his truck 3 hours from Dallas towards Kansas City and stopped at a truck stop to get dinner. At the truck stop he met Erwin, who had driven 4 hours from Kansas City towards Dallas. The distance between Dallas and Kansas City is 542 miles, and Erwin’s speed was eight miles per hour slower than Saul’s speed. Find the speed of the two truckers.In the following exercises, solve. 288. Charlie and Violet met for lunch at a restaurant between Memphis and New Orleans. Charlie had left Memphis and drove 4.8 hours towards New Orleans. Violet had left New Orleans and drove 2 hours towards Memphis, at a speed 10 miles per hour faster than Charlie’s speed. The distance between Memphis and New Orleans is 394 miles. Find the speed of the two drivers.In the following exercises, solve. 289. Sisters Helen and Anne live 332 miles apart. For Thanksgiving, they met at their other sister’s house partway between their homes. Helen drove 3.2 hours and Anne drove 2.8 hours. Helen’s average speed was four miles per hour faster than Anne’s. Find Helen’s average speed and Anne’s average speed.In the following exercises, solve. 290. Ethan and Leo start riding their bikes at the opposite ends of a 65-mile bike path. After Ethan has ridden 1.5 hours and Leo has ridden 2 hours, they meet on the path. Ethan’s speed is six miles per hour faster than Leo’s speed. Find the speed of the two bikers.In the following exercises, solve. 291. Elvira and Aletheia live 3.1 miles apart on the same street. They are in a study group that meets at a coffee shop between their houses. It took Elvira half an hour and Aletheia two-thirds of an hour to walk to the coffee shop. Aletheia’s speed is 0.6 miles per hour slower than Elvira’s speed. Find both women’s walking speeds.In the following exercises, solve. 292. DaMarcus and Fabian live 23 miles apart and play soccer at a park between their homes. DaMarcus rode his bike for threequarters of an hour and Fabian rode his bike for half an hour to get to the park. Fabian’s speed was six miles per hour faster than DaMarcus’ speed. Find the speed of both soccer players.In the following exercises, solve. 293. Cindy and Richard leave their dorm in Charleston at the same time. Cindy rides her bicycle north at a speed of 18 miles per hour. Richard rides his bicycle south at a speed of 14 miles per hour. How long will it take them to be 96 miles apart?In the following exercises, solve. 294. Matt and Chris leave their uncle’s house in Phoenix at the same time. Matt drives west on I-60 at a speed of 76 miles per hour. Chris drives east on I-60 at a speed of 82 miles per hour. How many hours will it take them to be 632 miles apart?In the following exercises, solve. 295. Two busses leave Billings at the same time. The Seattle bus heads west on I-90 at a speed of 73 miles per hour while the Chicago bus heads east at a speed of 79 miles an hour. How many hours will it take them to be 532 miles apart?In the following exercises, solve. 296. Two boats leave the same dock in Cairo at the same time. One heads north on the Mississippi River while the other heads south. The northboundboat travels four miles per hour. The southbound boat goes eight miles per hour. How long will it take them to be 54 miles apart?In the following exercises, solve. 297. Lorena walks the path around the park in 30 minutes. If she jogs, it takes her 20 minutes. Her jogging speed is 1.5 miles per hour faster than her walking speed. Find Lorena’s walking speed and jogging speed.In the following exercises, solve. 298. Julian rides his bike uphill for 45 minutes, then turns around and rides back downhill. It takes him 15 minutes to get back to where he started. His uphill speed is 3.2 miles per hour slower than his downhill speed. Find Julian’s uphill and downhill speed.In the following exercises, solve. 299. Cassius drives his boat upstream for 45 minutes. It takes him 30 minutes to return downstream. His speed going upstream is three miles per hour slower than his speed going downstream. Find his upstream and downstream speeds.In the following exercises, solve. 300. It takes Darline 20 minutes to drive to work in light traffic. To come home, when there is heavy traffic, it takes her 36 minutes. Her speed in light traffic is 24 miles per hour faster than her speed in heavy traffic. Find her speed in light traffic and in heavy traffic.In the following exercises, solve. 301. At 1:30 Marlon left his house to go to the beach, a distance of 7.6 miles. He rode his skateboard until 2:15, then walked the rest of the way. He arrived at the beach at 3:00. Marlon’s speed on his skateboard is 2.5 times his walking speed. Find his speed when skateboarding and when walking.In the following exercises, solve. 302. Aaron left at 9:15 to drive to his mountain cabin 108 miles away. He drove on the freeway until 10:45, and then he drove on the mountain road. He arrived at 11:05. His speed on the freeway was three times his speed on the mountain road. Find Aaron’s speed on the freeway and on the mountain road.In the following exercises, solve. 303. Marisol left Los Angeles at 2:30 to drive to Santa Barbara, a distance of 95 miles. The traffic was heavy until 3:20. She drove the rest of the way in very light traffic and arrived at 4:20. Her speed in heavy traffic was 40 miles per hour slower than her speed in light traffic. Find her speed in heavy traffic and in light traffic.In the following exercises, solve. 304. Lizette is training for a marathon. At 7:00 she left her house and ran until 8:15, then she walked until 11:15. She covered a total distance of 19 miles. Her running speed was five miles per hour faster than her walking speed. Find her running and walking speeds.John left his house in Irvine at 8:35 am to drive to a meeting in Los Angeles, 45 miles away. He arrived at the meeting at 9:50. At 3:30 pm, he left the meeting and drove home. He arrived home at 5:18. (a) What was his average speed on the drive from Irvine to Los Angeles? (b) What was his average speed on the drive from Los Angeles to Irvine? (c) What was the total time he spent driving to and from this meeting? (d) John drove a total of 90 miles roundtrip. Find his average speed. (Round to the nearest tenth.)Sarah wants to arrive at her friend’s wedding at3:00. The distance from Sarah’s house to the weddingis 95 miles. Based on usual traffic patterns, Sarahpredicts she can drive the first 15 miles at 60 miles per hour, the next 10 miles at 30 miles per hour, and the remainder of the drive at 70 miles per hour. (a) How long will it take Sarah to drive the first 15 miles? (b) How long will it take Sarah to drive the next 10 miles? (c) How long will it take Sarah to drive the rest of the trip? (d) What time should Sarah leave her house?When solving a uniform motion problem, how does drawing a diagram of the situation help you?When solving a uniform motion problem, how does creating a table help you?Alan is loading a pallet with boxes that each weighs 45 pounds. The pallet can safely support no more than 900 pounds. How many boxes can he safely load onto the pallet?The elevator in Yehire’s apartment building has a sign that says the maximum weight is 2,100 pounds. If the average weight of one person is 150 pounds, how many people can safely ride the elevator?Angie has $20 to spend on juice boxes for her son’s preschool picnic. Each pack of juice boxes costs $2.63. What is the maximum number of packs she can buy?Daniel wants to surprise his girlfriend with a birthday party at her favorite restaurant. It will cost $42.75 per person for dinner, including tip and tax. His budget for the party is $500. What is the maximum number of people Daniel can have at the party?Tiffany just graduated from college and her new job will pay her $20,000 per year plus 2% of all sales. She wants to earn at least $100,000 per year. For what total sales will she be able to achieve her goal?Christian has been offered a new job that pays $24,000 a year plus 3% of sales. For what total sales would this new job pay more than his current job which pays $60,000?Taleisha’s phone plan costs her $28.80 a month plus $0.20 per text message. How many text messages can she use and keep her monthly phone bill no more than $50?Rameen’s heating bill is $5.42 per month plus $1.08 per therm. How many therms can Rameen use if he wants his heating bill to be a maximum of $87.50?Caleb has a pet sitting business. He charges $32 per hour. His monthly expenses are $2,272. How many hours must he work in order to earn a profit of at least $800 per month?Felicity has a calligraphy business. She charges $2.50 per wedding invitation. Her monthly expenses are $650. How many invitations must she write to earn a profit of at least $2,800 per month?Malik is planning a 6-day summer vacation trip. He has $840 in savings, and he earns $45 per hour for tutoring. The trip will cost him $525 for airfare, $780 for food and sightseeing, and $95 per night for the hotel. How many hours must he tutor to have enough money to pay for the trip?Josue wants to go on a 10-day road trip next spring. It will cost him $180 for gas, $450 for food, and $49 per night for a motel. He has $520 in savings and can earn $30 per driveway shoveling snow. How many driveways must he shovel to have enough money to pay for the trip?In the following exercises, solve. 309. Mona is planning her son’s birthday party and has a budget of $285. The Fun Zone charges $19 per child. How many children can she have at the party and stay within her budget?In the following exercises, solve. 310. Carlos is looking at apartments with three of his friends. They want the monthly rent to be no more than $2360. If the roommates split the rent evenly among the four of them, what is the maximum rent each will pay?In the following exercises, solve. 311. A water taxi has a maximum load of 1,800 pounds. If the average weight of one person is 150 pounds, how many people can safely ride in the water taxi?In the following exercises, solve. 312. Marcela is registering for her college classes, which cost $105 per unit. How many units can she take to have a maximum cost of $1,365?In the following exercises, solve. 313. Arleen got a $20 gift card for the coffee shop. Her favorite iced drink costs $3.79. What is the maximum number of drinks she can buy with the gift card?In the following exercises, solve. 314. Teegan likes to play golf. He has budgeted $60 next month for the driving range. It costs him $10.55 for a bucket of balls each time he goes. What is the maximum number of times he can go to the driving range next month?In the following exercises, solve. 315. Joni sells kitchen aprons online for $32.50 each. How many aprons must she sell next month if she wants to earn at least $1,000?In the following exercises, solve. 316. Ryan charges his neighbors $17.50 to wash their car. How many cars must he wash next summer if his goal is to earn at least $1,500?In the following exercises, solve. 317. Keshad gets paid $2,400 per month plus 6% of his sales. His brother earns $3,300 per month. For what amount of total sales will Keshad’s monthly pay be higher than his brother’s monthly pay?In the following exercises, solve. 318. Kimuyen needs to earn $4,150 per month in order to pay all her expenses. Her job pays her $3,475 per month plus 4% of her total sales. What is the minimum Kimuyen’s total sales must be in order for her to pay all her expenses?In the following exercises, solve. 319. Andre has been offered an entry-level job. The company offered him $48,000 per year plus 3.5% of his total sales. Andre knows that the average pay for this job is $62,000. What would Andre’s total sales need to be for his pay to be at least as high as the average pay for this job?In the following exercises, solve. 320. Nataly is considering two job offers. The first job would pay her $83,000 per year. The second would pay her $66,500 plus 15% of her total sales. What would her total sales need to be for her salary on the second offer behigher than the first?In the following exercises, solve. 321. Jake’s water bill is $24.80 per month plus $2.20 per ccf (hundred cubic feet) of water. What is the maximum number of ccf Jake can use if he wants his bill to be no more than $60?In the following exercises, solve. 322. Kiyoshi’s phone plan costs $17.50 per month plus $0.15 per text message. What is the maximum number of text messages Kiyoshi can use so the phone bill is no more than $56.50?In the following exercises, solve. 323. Marlon’s TV plan costs $49.99 per month plus $5.49 per first-run movie. How many first-run movies can he watch if he wants to keep his monthly bill to be a maximum of $100?In the following exercises, solve. 324. Kellen wants to rent a banquet room in a restaurant for her cousin’s baby shower. The restaurant charges $350 for the banquet room plus $32.50 per person for lunch. How many people can Kellen have at the shower if she wants the maximum cost to be $1,500?In the following exercises, solve. 325. Moshde runs a hairstyling business from her house. She charges $45 for a haircut and style. Her monthly expenses are $960. She wants to be able to put at least $1,200 per month into her savings account order to open her own salon. How many “cut & styles” must she do to save at least $1,200 per month?In the following exercises, solve. 326. Noeinstalls and configures software on home computers. He charges $125 per job. His monthly expenses are $1,600. How many jobs must he work in order to make a profit of at least $2,400?In the following exercises, solve. 327. Katherine is a personal chef. She charges $115 per four-person meal. Her monthly expenses are $3,150. How many four-person meals must she sell in order to make a profit of at least $1,900?In the following exercises, solve. 328. Melissa makes necklaces and sells them online. She charges $88 per necklace. Her monthly expenses are $3745. How many necklaces must she sell if she wants to make a profit of at least $1,650?In the following exercises, solve. 329. Five student government officers want to go to the state convention. It will cost them $110 for registration, $375 for transportation and food, and $42 per person for the hotel. There is $450 budgeted for the convention in the student government savings account. They can earn the rest of the money they need by having a car wash. If they charge $5 per car, how many cars must they wash in order to have enough money to pay for the trip?In the following exercises, solve. 330. Cesar is planning a 4-day trip to visit his friend at a college in another state. It will cost him $198 for airfare, $56 for local transportation, and $45 per day for food. He has $189 in savings and can earn $35 for each lawn he mows. How many lawns must he mow to have enough money to pay for the trip?In the following exercises, solve. 331. Alonzo works as a car detailer. He charges $175 per car. He is planning to move out of his parents’ house and rent his first apartment. He will need to pay $120 for application fees, $950 for security deposit, and first and last months’ rent at $1,140 per month. He has $1,810 in savings. How many cars must he detail to have enough money to rent the apartment?In the following exercises, solve. 332. Eun-Kyung works as a tutor and earns $60 per hour. She has $792 in savings. She is planning an anniversary party for her parents. She would like to invite 40 guests. The party will cost her $1,520 for food and drinks and $150 for the photographer. She will also have a favor for each of the guests, and each favor will cost $7.50. How many hours must she tutor to have enough money for the party?Maximum Load on a Stage In 2014, a high school stage collapsed in Fullerton, California, when 250 students got on stage for the finale of a musical production. Two dozen students were injured. The stage could support a maximum of 12,750 pounds. If the average weight of a student is assumed to be 140 pounds, what is the maximum number of students who could safely be on the stage?Maximum Weight on a Boat In 2004, a water taxi sank in Baltimore harbor and five people drowned. The water taxi had a maximum capacity of 3,500 pounds (25 people with average weight 140 pounds). The average weight of the 25 people on the water taxi when it sank was 168 pounds per person. What should the maximum number of people of this weight have been?Wedding Budget Adele and Walter found the perfect venue for their wedding reception. The cost is $9,850 for up to 100 guests, plus $38 for each additional guest. How many guests can attend if Adele and Walter want the total cost to be no more than $12,500?Shower Budget Penny is planning a baby shower for her daughter-in-law. The restaurant charges $950 for up to 25 guests, plus $31.95 for each additional guest. How many guests can attend if Penny wants the total cost to be no more than $1,500?Find your last month’s phone bill and the hourly salary you are paid at your job. (If you do not have a job, use the hourly salary you would realistically be paid if you had a job.) Calculate the number of hours of work it would take you to earn at least enough money to pay your phone bill by writing an appropriate inequality and then solving it.In the following exercises, reflect on your approach to word problems. 339. How has your attitude towards solving word problems changed as a result of working through this chapter? Explain.In the following exercises, reflect on your approach to word problems. 340. Did the problem-solving strategy help you solve word problems in this chapter? Explain.In the following exercises, solve using the problem-solving strategy for word problems. Remember to write a complete sentence to answer each question. 341. Three-fourths of the people at a concert are children. If there are 87 children, what is the total number of people at the concert?In the following exercises, solve using the problem-solving strategy for word problems. Remember to write a complete sentence to answer each question. 342. There are nine saxophone players in the band. The number of saxophone players is one less than twice the number of tuba players. Find the number of tuba players.In the following exercises, solve each number word problem. 343. The sum of a number and three is forty-one. Find the number.In the following exercises, solve each number word problem. 344. Twice the difference of a number and ten is fifty-four. Find the number.In the following exercises, solve each number word problem. 345. One number is nine less than another. Their sum is negative twenty-seven. Find the numbers.In the following exercises, solve each number word problem. 346. One number is eleven more than another. If their sum is increased by seventeen, the result is 90. Find the numbers.In the following exercises, solve each number word problem. 347. One number is two more than four times another. Their sum is 13 . Find the numbers.In the following exercises, solve each number word problem. 348. The sum of two consecutive integers is 135 . Find the numbers.In the following exercises, solve each number word problem. 349. Find three consecutive integers whose sum is 141 .In the following exercises, solve each number word problem. 350. Find three consecutive even integers whose sum is 234.In the following exercises, solve each number word problem. 351. Find three consecutive odd integers whose sum is 51.In the following exercises, solve each number word problem. 352. Koji has $5,502 in his savings account. This is $30 less than six times the amount in his checking account. How much money does Koji have in his checking account?In the following exercises, translate and solve. 353. What number is 67% of 250?In the following exercises, translate and solve. 354. 300% of 82 is what number?In the following exercises, translate and solve. 355. 12.5% of what number is 20?In the following exercises, translate and solve. 356. 72 is 30% of what number?In the following exercises, translate and solve. 357. What percent of 125 is 150?In the following exercises, translate and solve. 358. 127.5 is what percent of 850?In the following exercises, solve. 359. The bill for Dino’s lunch was $19.45. He wanted to leave 20% of the total bill as a tip. How muchshould the tip be?In the following exercises, solve. 360. Reza was very sick and lost 15% of his original weight. He lost 27 pounds. What was his original weight?In the following exercises, solve. 361. Dolores bought a crib on sale for $350. The sale price was 40% of the original price. What was the original price of the crib?In the following exercises, solve. 362. Jaden earns $2,680 per month. He pays $938 a month for rent. What percent of his monthly pay goes to rent?In the following exercises, solve. 363. Angel’s got a raise in his annual salary from $55,400 to $56,785. Find the percent increase.In the following exercises, solve. 364. Rowena’s monthly gasoline bill dropped from $83.75 last month to $56.95 this month. Find the percent decrease.In the following exercises, solve. 365. Winston deposited $3,294 in a bank account with interest rate 2.6%. How much interest was earned in 5 years?In the following exercises, solve. 366. Moira borrowed $4,500 from her grandfather to pay for her first year of college. Three years later, she repaid the $4,500 plus $243 interest. What was the rate of interest?In the following exercises, solve. 367. Jaime’s refrigerator loan statement said he would pay $1,026 in interest for a 4-year loan at 13.5%. How much did Jaime borrow to buy the refrigerator?In the following exercises, solve. 368. In 12 years, a bond that paid 6.35% interest earned $7,620 interest. What was the principal of the bond?In the following exercises, find the sale price. 369. The original price of a handbag was $84. Carole bought it on sale for $21 off.In the following exercises, find the sale price. 370. Marian wants to buy a coffee table that costs $495. Next week the coffee table will be on sale for $149 off.In the following exercises, find (a) the amount of discount and (b) the sale price. 371. Emmett bought a pair of shoes on sale at 40% off from an original price of $138.In the following exercises, find (a) the amount of discount and (b) the sale price. 372. Anastasia bought a dress on sale at 75% off from an original price of $280.In the following exercises, find (a) the amount of discount and (b) the discount rate. (Round to the nearest tenth of a percent, if needed.) 373. Zack bought a printer for his office that was on sale for $380. The original price of the printer was $450.In the following exercises, find (a) the amount of discount and (b) the discount rate. (Round to the nearest tenth of a percent, if needed.) 374. Lacey bought a pair of boots on sale for $95. The original price of the boots was $200.In the following exercises, find (a) the amount of the mark-up and (b) the list price. 375. Nga and Lauren bought a chest at a flea market for $50. They re-finished it and then added a 350% mark-up.In the following exercises, find (a) the amount of the mark-up and (b) the list price. 376. Carly bought bottled water for $0.24 per bottle at the discount store. She added a 75% mark-up before selling them at the football game.In the following exercises, solve each coin word problem. 377. Francie has $4.35 in dimes and quarters. The number of dimes is five more than the number of quarters. How many of each coin does she have?In the following exercises, solve each coin word problem. 378. Scott has $0.39 in pennies and nickels. The number of pennies is eight times the number of nickels. How many of each coin does he have?In the following exercises, solve each coin word problem. 379. Paulette has $140 in $5 and $10 bills. The number of $10 bills is one less than twice the number of $5 bills. How many of each does she have?In the following exercises, solve each coin word problem. 380. Lenny has $3.69 in pennies, dimes, and quarters. The number of pennies is three more than the number of dimes. The number of quarters is twice the number of dimes. How many of each coin does he have?In the following exercises, solve each ticket or stamp word problem. 381. A church luncheon made $842. Adult tickets cost $10 each and children’s tickets cost $6 each. The number of children was 12 more than twice the number of adults. How many of each ticket were sold?In the following exercises, solve each ticket or stamp word problem. 382. Tickets for a basketball game cost $2 for students and $5 for adults. The number of students was three less than 10 times the number of adults. The total amount of money from ticket sales was $619. How many of each ticket were sold?In the following exercises, solve each ticket or stamp word problem. 383. 125 tickets were sold for the jazz band concert for a total of $1,022. Student tickets cost $6 each and general admission tickets cost $10 each. How many of each kind of ticket were sold?In the following exercises, solve each ticket or stamp word problem. 384. One afternoon the water park sold 525 tickets for a total of $13,545. Child tickets cost $19 each and adult tickets cost $40 each. How many of each kind of ticket were sold?In the following exercises, solve each ticket or stamp word problem. 385. Ana spent $4.06 buying stamps. The number of $0.41 stamps she bought was five more than the number of $0.26 stamps. How many of each did she buy?In the following exercises, solve each ticket or stamp word problem. 386. Yumi spent $34.15 buying stamps. The number of $0.56 stamps she bought was 10 less than four times the number of $0.41 stamps. How many of each did she buy?In the following exercises, solve each mixture word problem. 387. Marquese is making 10 pounds of trail mix from raisins and nuts. Raisins cost $3.45 per pound and nuts cost $7.95 per pound. How many pounds of raisins and how many pounds of nuts should Marquese use for the trail mix to cost him $6.96 per pound?In the following exercises, solve each mixture word problem. 388. Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tile. She will use basic tiles that cost $8 per square foot and decorator tiles that cost $20 per square foot. How many square feet of each tile should she use so that the overall cost of the backsplash will be $10 per square foot?In the following exercises, solve each mixture word problem. 389. Shawn has $15,000 to invest. She will put some of it into a fund that pays 4.5% annual interest and the rest in a certificate of deposit that pays 1.8% annual interest. How much should she invest in each account if she wants to earn 4.05% annual interest on the total amount?In the following exercises, solve each mixture word problem. 390. Enrique borrowed $23,500 to buy a car. He pays his uncle 2% interest on the $4,500 he borrowed from him, and he pays the bank 11.5% interest on the rest. What average interest rate does he pay on the total $23,500? (Round your answer to the nearest tenth of a percent.)In the following exercises, solve using triangle properties. 391. The measures of two angles of a triangle are 22 and 85 degrees. Find the measure of the third angle.In the following exercises, solve using triangle properties. 392. The playground at a shopping mall is a triangle with perimeter 48 feet. The lengths of two sides are 19 feet and 14 feet. How long is the third side?In the following exercises, solve using triangle properties. 393. A triangular road sign has base 30 inches and height 40 inches. What is its area?In the following exercises, solve using triangle properties. 394. What is the height of a triangle with area 67.5 square meters and base 9 meters?In the following exercises, solve using triangle properties. 395. One angle of a triangle is 30° more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles.In the following exercises, solve using triangle properties. 396. One angle of a right triangle measures 58°. What is the measure of the other angles of the triangle?In the following exercises, solve using triangle properties. 397. The measure of the smallest angle in a right triangle is 45° less than the measure of the next larger angle. Find the measures of all three angles.In the following exercises, solve using triangle properties. 398. The perimeter of a triangle is 97 feet. One side of the triangle is eleven feet more than the smallest side. The third side is six feet more than twice the smallest side. Find the lengths of all sides.In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse. 399.In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse. 400.In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary. 401.In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary. 402.In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary. 403.In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary. 404.In the following exercises, solve. Approximate to the nearest tenth, if necessary. 405. Sergio needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure. The antenna is 8 feet tall and Sergio has 10 feet of wire. How far from the base of the antenna can he attach the wire?In the following exercises, solve. Approximate to the nearest tenth, if necessary. 406. Seong is building shelving in his garage. The shelves are 36 inches wide and 15 inches tall. He wants to put a diagonal brace across the back to stabilize the shelves, as shown. How long should the brace be?In the following exercises, solve using rectangle properties. 407. The length of a rectangle is 36 feet and the width is 19 feet. Find the (a) perimeter (b) area.In the following exercises, solve using rectangle properties. 408. A sidewalk in front of Kathy’s house is in the shape of a rectangle four feet wide by 45 feet long. Find the (a) perimeter (b)area.In the following exercises, solve using rectangle properties. 409. The area of a rectangle is 2356 square meters. The length is 38 meters. What is the width?In the following exercises, solve using rectangle properties. 410. The width of a rectangle is 45 centimeters. The area is 2,700 square centimeters. What is the length?In the following exercises, solve using rectangle properties. 411. The length of a rectangle is 12 cm more than the width. The perimeter is 74 cm. Find the length and the width.In the following exercises, solve using rectangle properties. 412. The width of a rectangle is three more than twice the length. The perimeter is 96 inches. Find the length and the width.In the following exercises, solve. 413. When Gabe drives from Sacramento to Redding it takes him 2.2 hours. It takes Elsa 2 hours to drive the same distance. Elsa’s speed is seven miles per hour faster than Gabe’s speed. Find Gabe’s speed and Elsa’s speed.In the following exercises, solve. 414. Louellen and Tracy met at a restaurant on the road between Chicago and Nashville. Louellen had left Chicago and drove 3.2 hours towards Nashville. Tracy had left Nashville and drove 4 hours towards Chicago, at a speed one mile per hour faster than Louellen’s speed. The distance between Chicago and Nashville is 472 miles. Find Louellen’s speed and Tracy’s speed.In the following exercises, solve. 415. Two busses leave Amarillo at the same time. The Albuquerque bus heads west on the I-40 at a speed of 72 miles per hour, and the Oklahoma City bus heads east on the I-40 at a speed of 78 miles per hour. How many hours will it take them to be 375 miles apart?In the following exercises, solve. 416. Kyle rowed his boat upstream for 50 minutes. It took him 30 minutes to row back downstream. His speed going upstream is two miles per hour slower than his speed going downstream. Find Kyle’s upstream and downstream speeds.