Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Elementary Algebra
In the following exercises, translate to a system of equations and solve. 229. A motor boat traveled 18 miles down a river in two hours but going back upstream, it took 4.5 hours due to the current. Find the rate of the motor boat in still water and the rate of the current. (Round to the nearest hundredth.).In the following exercises, translate to a system of equations and solve. 230. A river cruise boat sailed 80 miles down the Mississippi River for four hours. It took five hours to return. Find the rate of the cruise boat in still water and the rate of the current. (Round to the nearest hundredth.).In the following exercises, translate to a system of equations and solve. 231. A small jet can fly 1,072 miles in 4 hours with a tailwind but only 848 miles in 4 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.In the following exercises, translate to a system of equations and solve. 232. A small jet can fly 1,435 miles in 5 hours with a tailwind but only 1215 miles in 5 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.In the following exercises, translate to a system of equations and solve. 233. A commercial jet can fly 868 miles in 2 hours with a tailwind but only 792 miles in 2 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.In the following exercises, translate to a system of equations and solve. 234. A commercial jet can fly 1,320 miles in 3 hours with a tailwind but only 1,170 miles in 3 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.At a school concert, 425 tickets were sold. Student tickets cost $5 each and adult tickets cost $8 each. The total receipts for the concert were $2,851. Solve the system {s+a=4255s+8a=2,851 to find s, the number of student tickets and a, the number of adult tickets.The first graders at one school went on a field trip to the zoo. The total number of children and adults who went on the field trip was 115. The number of adults was 14 the number of children. Solve the system {c+a=115a= 1 4c to find c, the number of children and a, the number of adults.Write an application problem similar to Example5.37 using the ages of two of your friends or family members. Then translate to a system of equations and solve it.Write a uniform motion problem similar to Example 5.42 that relates to where you live with your friends or family members. Then translate to a system of equations and solve it.Translate to a system of equations and solve: The ticket office at the zoo sold 553 tickets one day. The receipts totaled $3,936. How many $9 adult tickets and how many $6 child tickets were sold?Translate to a system of equations and solve: A science center sold 1,363 tickets on a busy weekend. The receipts totaled $12,146. How many $12 adult tickets and how many $7 child tickets were sold?Translate to a system of equations and solve: Matilda has a handful of quarters and dimes, with a total value of $8.55. The number of quarters is 3 more than twice the number of dimes. How many dimes and how many quarters does she have?Translate to a system of equations and solve: Juan has a pocketful of nickels and dimes. The total value of the coins is $8.10. The number of dimes is 9 less than twice the number of nickels. How many nickels and how many dimes does Juan have?Translate to a system of equations and solve: Greta wants to make 5 pounds of a nut mix using peanuts and cashews. Her budget requires the mixture to cost her $6 per pound. Peanuts are $4 per pound and cashews are $9 per pound. How many pounds of peanuts and how many pounds of cashews should she use?Translate to a system of equations and solve: Sammy has most of the ingredients he needs to make a large batch of chili. The only items he lacks are beans and ground beef. He needs a total of 20 pounds combined of beans and ground beef and has a budget of $3 per pound. The price of beans is $1 per pound and the price of ground beef is $5 per pound. How many pounds of beans and how many pounds of ground beef should he purchase?Translate to a system of equations and solve: LeBron needs 150 milliliters of a 30% solution of sulfuric acid for a lab experiment but only has access to a 25% and a 50% solution. How much of the 25% and how much of the 50% solution should he mix to make the 30% solution?Translate to a system of equations and solve: Anatole needs to make 250 milliliters of a 25% solution of hydrochloric acid for a lab experiment. The lab only has a 10% solution and a 40% solution in the storeroom. How much of the 10% and how much of the 40% solutions should he mix to make the 25% solution?Translate to a system of equations and solve: Leon had $50,000 to invest and hopes to earn 6.2 % interest per year. He will put some of the money into a stock fund that earns 7% per year and the rest in to a savings account that earns 2% per year. How much money should he put into each fund?Translate to a system of equations and solve: Julius invested $7,000 into two stock investments. One stock paid 11% interest and the other stock paid 13% interest. He earned 12.5% interest on the total investment. How much money did he put in each stock?Translate to a system of equations and solve: Laura owes $18,000 on her student loans. The interest rate on the bank loan is 2.5% and the interest rate on the federal loan is 6.9 %. The total amount of interest she paid last year was $1,066. What was the principal for each loan?Translate to a system of equations and solve: Jill’s Sandwich Shoppe owes $65,200 on two business loans, one at 4.5% interest and the other at 7.2% interest. The total amount of interest owed last year was $3,582. What was the principal for each loan?In the following exercises, translate to a system of equations and solve. 239. Tickets to a Broadway show cost $35 for adults and $15 for children. The total receipts for 1650 tickets at one performance were $47,150. How many adult and how many child tickets were sold?In the following exercises, translate to a system of equations and solve. 240. Tickets for a show are $70 for adults and $50 for children. One evening performance had a total of 300 tickets sold and the receipts totaled $17,200. How many adult and how many child tickets were sold?In the following exercises, translate to a system of equations and solve. 241. Tickets for a train cost $10 for children and $22 for adults. Josie paid $1,200 for a total of 72 tickets. How many children’s tickets and how many adult tickets did Josie buy?In the following exercises, translate to a system of equations and solve. 242. Tickets for a baseball gameare $69 for Main Level seats and$39 for Terrace Level seats. A group of sixteen friends went to the game and spent a total of $804 for the tickets. How many of Main Level and how many Terrace Level tickets did they buy?In the following exercises, translate to a system of equations and solve. 243. Tickets for a dance recital cost $15 for adults and $7 for children. The dance company sold 253 tickets and the total receipts were $2,771. How many adult tickets and how many child tickets were sold?In the following exercises, translate to a system of equations and solve. 244. Tickets for the community fair cost $12 for adults and $5 dollars for children. On the first day of the fair, 312 tickets were sold for a total of $2,204. How many adult tickets and how many child tickets were sold?In the following exercises, translate to a system of equations and solve. 245. Brandon has a cup of quarters and dimes with a total value of $3.80. The number of quarters is four less than twice the number of quarters. How many quarters and how many dimes does Brandon have?In the following exercises, translate to a system of equations and solve. 246. Sherri saves nickels and dimes in a coin purse for her daughter. The total value of the coins in the purse is $0.95. The number of nickels is two less than five times the number of dimes. How many nickels and how many dimes are in the coin purse?In the following exercises, translate to a system of equations and solve. 247. Peter has been saving his loose change for several days. When he counted his quarters and dimes, he found they had a total value $13.10. The number of quarters was fifteen more than three times the number of dimes. How many quarters and how many dimes did Peter have?In the following exercises, translate to a system of equations and solve. 248. Lucinda had a pocketful ofdimes and quarters with a valueof $ $6.20. The number of dimes is eighteen more than three times the number of quarters. How many dimes and how many quarters does Lucinda have?In the following exercises, translate to a system of equations and solve. 249. A cashier has 30 bills, all of which are $10 or $20 bills. The total value of the money is $460. How many of each type of bill does the cashier have?In the following exercises, translate to a system of equations and solve. 250. A cashier has 54 bills, all of which are $10 or $20 bills. The total value of the money is $910. How many of each type of bill does the cashier have?In the following exercises, translate to a system of equations and solve. 251. Marissa wants to blend candy selling for $1.80 per pound with candy costing $1.20 per pound to get a mixture that costs her $1.40 per pound to make. She wants to make 90 pounds of the candy blend. How many pounds of each type of candy should she use?In the following exercises, translate to a system of equations and solve. 252. How many pounds of nuts selling for $6 per pound and raisins selling for $3 per pound should Kurt combine to obtain 120 pounds of trail mix that cost him $5 per pound?In the following exercises, translate to a system of equations and solve. 253. Hannah has to make twenty-five gallons of punch for a potluck. The punch is made of soda and fruit drink. The cost of the soda is $1.79 per gallon and the cost of the fruit drink is $2.49 per gallon. Hannah’s budget requires that the punch cost $2.21 per gallon. How many gallons of soda and how many gallons of fruit drink does she need?In the following exercises, translate to a system of equations and solve. 254. Joseph would like to make 12 pounds of a coffee blend at a cost of $6.25 per pound. He blends Ground Chicory at $4.40 a pound with Jamaican Blue Mountain at $8.84 per pound. How much of each type of coffee should he use?In the following exercises, translate to a system of equations and solve. 255. Julia and her husband own a coffee shop. They experimented with mixing a City Roast Columbian coffee that cost $7.80 per pound with French Roast Columbian coffee that cost $8.10 per pound to make a 20 pound blend. Their blend should cost them $7.92 per pound. How much of each type of coffee should they buy?In the following exercises, translate to a system of equations and solve. 256. Melody wants to sell bags of mixed candy at her lemonade stand. She will mix chocolate pieces that cost $4.89 per bag with peanut butter pieces that cost $3.79 per bag to get a total of twenty-five bags of mixed candy. Melody wants the bags of mixed candy to cost her $4.23 a bag to make. How many bags of chocolate pieces and how many bags of peanut butter pieces should she use?In the following exercises, translate to a system of equations and solve. 257. Jotham needs 70 liters of a 50% alcohol solution. He has a 30% and an 80% solution available. How many liters of the 30% and how many liters of the 80% solutions should he mix to make the 50% solution?In the following exercises, translate to a system of equations and solve. 258. Joy is preparing 15 liters of a 25% saline solution. She only has 40% and 10% solution in her lab. How many liters of the 40% and how many liters of the 10% should she mix to make the 25% solution?In the following exercises, translate to a system of equations and solve. 259. A scientist needs 65 liters of a 15% alcohol solution. She has available a 25% and a 12% solution. How many liters of the 25% and how many liters of the 12% solutions should she mix to make the 15% solution?In the following exercises, translate to a system of equations and solve. 260. A scientist needs 120 milliliters of a 20% acid solution for an experiment. The lab has available a 25% and a 10% solution. How many liters of the 25% and how many liters of the 10% solutions should the scientist mix to make the 20% solution?In the following exercises, translate to a system of equations and solve. 261. A 40% antifreeze solution is to be mixed with a 70% antifreeze solution to get 240 liters of a 50% solution. How many liters of the 40% and how many liters of the 70% solutions will be used?In the following exercises, translate to a system of equations and solve. 262. A 90% antifreeze solution is to be mixed with a 75% antifreeze solution to get 360 liters of a 85% solution. How many liters of the 90% and how many liters of the 75% solutions will be used?In the following exercises, translate to a system of equations and solve. 263. Hattie had $3,000 to invest and wants to earn 10.6% interest per year. She will put some of the money into an account that earns 12% per year and the rest into an account that earns 10% per year. How much money should she put into each account?In the following exercises, translate to a system of equations and solve. 264. Carol invested $2,560 into two accounts. One account paid 8% interest and the other paid 6% interest. She earned 7.25% interest on the total investment. How much money did she put in each account?In the following exercises, translate to a system of equations and solve. 265. Sam invested $48,000, some at 6% interest and the rest at 10%. How much did he invest at each rate if he received $4,000 in interest in one year?In the following exercises, translate to a system of equations and solve. 266. Arnold invested $64,000, some at 5.5% interest and the rest at 9%. How much did he invest at each rate if he received $4,500 in interest in one year?In the following exercises, translate to a system of equations and solve. 267. After four years in college, Josie owes $65,800 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owed for one year was $2,878.50. What is the amount of each loan?In the following exercises, translate to a system of equations and solve. 268. Mark wants to invest $10,000 to pay for his daughter’s wedding next year. He will invest some of the money in a short term CD that pays 12% interest and the rest in a money market savings account that pays 5% interest. How much should he invest at each rate if he wants to earn $1,095 in interest in one year?In the following exercises, translate to a system of equations and solve. 269. A trust fund worth $25,000 is invested in two different portfolios. This year, one portfolio is expected to earn 5.25% interest and the other is expected to earn 4%. Plans are for the total interest on the fund to be $1150 in one year. How much money should be invested at each rate?In the following exercises, translate to a system of equations and solve. 270. A business has two loans totaling $85,000. One loan has a rate of 6% and the other has a rate of 4.5%. This year, the business expects to pay $4650 in interest on the two loans. How much is each loan?In the following exercises, translate to a system of equations and solve. 271. 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?In the following exercises, translate to a system of equations and solve. 272. As the treasurer of her daughter’s Girl Scout troop, Laney collected money for some girls and adults to go to a three-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?Take a handful of two types of coins, and write a problem similar to Example 5.46 relating the total number of coins and their total value. Set up a system of equations to describe your situation and then solve it.In Example 5.50 we solved the system ofequations {b+f=21,5400.105b+0.059f=1669.68 bysubstitution. Would you have used substitution or elimination to solve this system? Why?Determine whether the ordered pair is a solution to the system. {x5y102x+3y2 (a) (3,1) (b) (6,3)Determine whether the ordered pair is a solution to the system. {44x24xy20 (a) (2,1) (b) (4,1)Solve the system by graphing. {y3x+2yx1Solve the system by graphing. {y 1 2x+3y3x4Solve the system by graphing. {x+y2y 2 3x1Solve the system by graphing. {3x2y6y 1 4x+5Solve the system by graphing. {y3x2y1Solve the system by graphing. {x4x2y4Solve the system by graphing. {3x2y12y 3 2x+1Solve the system by graphing. {x+3y8y 1 3x2Solve the system by graphing. {y3x+13x+y4Solve the system by graphing. {y 1 4x+2x+4y4A trailer can carry a maximum weight of 160 pounds and a maximum volume of 15 cubic feet. A microwave oven weighs 30 pounds and has 2 cubic feet of volume, while a printer weighs 20 pounds and has 3 cubic feet of space. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Could 4 microwaves and 2 printers be carried on this trailer? (d) Could 7 microwaves and 3 printers be carried on this trailer?Mary needs to purchase supplies of answer sheets and pencils for a standardized test to be given to the juniors at her high school. The number of the answer sheets needed is at least 5 more than twice the number of pencils. The pencils cost $2 and the answer sheets cost $1. Mary’s budget for these supplies allows for a maximum cost of $400. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Could Mary purchase 100 pencils and 100 answer sheets? (d) Could Mary purchase 150 pencils and 150 answer sheets?Tension needs to eat at least an extra 1,000 calories a day to prepare for running a marathon. He has only $25 to spend on the extra food he needs and will spend it on $0.75 donuts which have 360 calories each and $2 energy drinks which have 110 calories. (a) Write a system of inequalities that models this situation. (b) Graph the system. (c) Can he buy 8 donuts and 4 energy drinks? (d) Can he buy 1 donut and 3 energy drinks?Philip’s doctor tells him he should add at least 1000 more calories per day to his usual diet. Philip wants to buy protein bars that cost $1.80 each and have 140 calories and juice that costs $1.25 per bottle and have 125 calories. He doesn’t want to spend more than $12. (a) Write a system of inequalities that models this situation. (b) Graph the system. (c) Can he buy 3 protein bars and 5 bottles of juice? (d) Can he buy 5 protein bars and 3 bottles of juice?In the following exercises, determine whether each ordered pair is a solution to the system. 275. {3x+y52xy10 (a) (3,3) (b) (7,1)In the following exercises, determine whether each ordered pair is a solution to the system. 276. {4xy102x+2y8 (a) (5,2) (b) (1,3)In the following exercises, determine whether each ordered pair is a solution to the system. 277. {y 2 3x5x+ 1 2y4 (a) (6,4) (b) (3,0)In the following exercises, determine whether each ordered pair is a solution to the system. 278. {y 3 2+3 3 4x2y5 (a) (4,1) (b) (8,3)In the following exercises, determine whether each ordered pair is a solution to the system. 279. {7x+2y145xy8 (a)(2,3) (b) (7,1)In the following exercises, determine whether each ordered pair is a solution to the system. 280. {6x5y202x+7y8 (a) (1,3) (b) (4,4)In the following exercises, determine whether each ordered pair is a solution to the system. 281. {2x+3y24x6y1 (a) (32,43) (b) (14,76)In the following exercises, determine whether each ordered pair is a solution to the system. 282. {5x3y210x+6y4 (a) (15,23) (b)(310,76)In the following exercises, solve each system by graphing. 283. {y3x+2yx1In the following exercises, solve each system by graphing. 284. {y2x+2yx1In the following exercises, solve each system by graphing. 285. {y2x1y 1 2x+4In the following exercises, solve each system by graphing. 286. {y 2 3x+2y2x3In the following exercises, solve each system by graphing. 287. {xy1y 1 4x+3In the following exercises, solve each system by graphing. 288. {x+2y4yx2In the following exercises, solve each system by graphing. 289. {3xy6y 1 2xIn the following exercises, solve each system by graphing. 290. {2x+4y8y 3 4xIn the following exercises, solve each system by graphing. 291. {2x5y103x+4y12In the following exercises, solve each system by graphing. 292. {3x2y64x2y8In the following exercises, solve each system by graphing. 293. {2x+2y4x+3y9In the following exercises, solve each system by graphing. 294. {2x+y6x+2y4In the following exercises, solve each system by graphing. 295. {x2y3y1In the following exercises, solve each system by graphing. 296. {x3y4y1In the following exercises, solve each system by graphing. 297. {y 1 2x3x2In the following exercises, solve each system by graphing. 298. {y 2 3x+5x3In the following exercises, solve each system by graphing. 299. {y 3 4x2y2In the following exercises, solve each system by graphing. 300. {y 1 2x+3y1In the following exercises, solve each system by graphing. 301. {3x4y8x1In the following exercises, solve each system by graphing. 302. {3x+5y10x1In the following exercises, solve each system by graphing. 303. {x3y2In the following exercises, solve each system by graphing. 304. {x1y3In the following exercises, solve each system by graphing. 305. {2x+4y4y 1 2x2In the following exercises, solve each system by graphing. 306. {x3y6y 1 3x+1In the following exercises, solve each system by graphing. 307. {2x+6y06y2x+4In the following exercises, solve each system by graphing. 308. {3x+6y124y2x4In the following exercises, solve each system by graphing. 309. {y3x+23x+y5In the following exercises, solve each system by graphing. 310. {y 1 2x12x+4y4In the following exercises, solve each system by graphing. 311. {y 1 4x2x+4y6In the following exercises, solve each system by graphing. 312. {y3x13x+y4In the following exercises, solve each system by graphing. 313. {3yx+22x+6y8In the following exercises, solve each system by graphing. 314. { y 3 4 x2 3x+4y7In the following exercises, translate to a system of inequalities and solve. 315. Caitlyn sells her drawings at the county fair. She wants to sell at least 60 drawings and has portraits and landscapes. She sells the portraits for $15 and the landscapes for $10. She needs to sell at least $800 worth of drawings in order to earn a profit. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Will she make a profit if she sells 20 portraits and 35 landscapes? (d) Will she make a profit if she sells 50 portraits and 20 landscapes?In the following exercises, translate to a system of inequalities and solve. 316. Jake does not want to spend more than $50 onbags of fertilizer and peat moss for his garden.Fertilizer costs $2 a bag and peat moss costs $5 a bag. Jake’s van can hold at most 20 bags. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Can he buy 15 bags of fertilizer and 4 bags of peat moss? (d) Can he buy 10 bags of fertilizer and 10 bags of peat moss?In the following exercises, translate to a system of inequalities and solve. 317. Reiko needs to mail her Christmas cards and packages and wants to keep her mailing costs to no more than $500. The number of cards is at least 4 more than twice the number of packages. The cost of mailing a card (with pictures enclosed) is $3 and for a package the cost is $7. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Can she mail 60 cards and 26 packages? (d) Can she mail 90 cards and 40 packages?In the following exercises, translate to a system of inequalities and solve. 318. Juan is studying for his final exams in Chemistry and Algebra. He knows he only has 24 hours to study, and it will take him at least three times as long to study for Algebra than Chemistry. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Can he spend 4 hours on Chemistry and 20 hours on Algebra? (d) Can he spend 6 hours on Chemistry and 18 hours on Algebra?In the following exercises, translate to a system of inequalities and solve. 319. Jocelyn is pregnant and needs to eat at least 500 more calories a day than usual. When buying groceries one day with a budget of $15 for the extra food, she buys bananas that have 90 calories each and chocolate granola bars that have 150 calories each. The bananas cost $0.35 each and the granola bars cost $2.50 each. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Could she buy 5 bananas and 6 granola bars? (d) Could she buy 3 bananas and 4 granola bars?In the following exercises, translate to a system of inequalities and solve. 320. Mark is attempting to build muscle mass and so he needs to eat at least an additional 80 grams of protein a day. A bottle of protein water costs $3.20 and a protein bar costs $1.75. The protein water supplies 27 grams of protein and the bar supplies 16 gram. If he has $ 10 dollars to spend (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Could he buy 3 bottles of protein water and 1 protein bar? (d) Could he buy no bottles of protein water and 5 protein bars?In the following exercises, translate to a system of inequalities and solve. 321. Jocelyn desires to increase both her protein consumption and caloric intake. She desires to have at least 35 more grams of protein each day and no more than an additional 200 calories daily. An ounce of cheddar cheese has 7 grams of protein and 110 calories. An ounce of parmesan cheese has 11 grams of protein and 22 calories. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Could she eat 1 ounce of cheddar cheese and 3 ounces of parmesan cheese? (d) Could she eat 2 ounces of cheddar cheese and 1 ounce of parmesan cheese?In the following exercises, translate to a system of inequalities and solve. 322. Mark is increasing his exercise routine by running and walking at least 4 miles each day. His goal is to burn a minimum of 1,500 calories from this exercise. Walking burns 270 calories/mile and running burns 650 calories. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Could he meet his goal by walking 3 miles and running 1 mile? (d) Could he meet his goal by walking 2 miles and running 2 mile?Tickets for an American Baseball League game for 3 adults and 3 children cost less than $75, while tickets for 2 adults and 4 children cost less than $62. (a) Write a system of inequalities to model this problem. (b) Graph the system. (c) Could the tickets cost $20 for adults and $8 for children? (d) Could the tickets cost $15 for adults and $5 for children?Grandpa and Grandma are treating their family to the movies. Matinee tickets cost $4 per child and $4 per adult. Evening tickets cost $6 per child and $8 per adult. They plan on spending no more than $80 on the matinee tickets and no more than $100 on the evening tickets. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Could they take 9 children and 4 adults to both shows? (d) Could they take 8 children and 5 adults to both shows?Graph the inequality xy3 . How do you knowwhich side of the line xy=3 should be shaded?Graph the system {x+2y6y 1 2x4 . What does the solution mean?In the following exercises, determine if the following points are solutions to the given system of equations. 327. {x+3y=92x4y=12 (a) (3,2) (b) (0,3)In the following exercises, determine if the following points are solutions to the given system of equations. 328. {x+y=8y=x4 (a) (6,2) (b)(9,1)In the following exercises, solve the following systems of equations by graphing. 329. {3x+y=6x+3y=6In the following exercises, solve the following systems of equations by graphing. 330.{y=x2y=2x2In the following exercises, solve the following systems of equations by graphing. 331. {2xy=6y=4In the following exercises, solve the following systems of equations by graphing. 332.{x+4y=1x=3In the following exercises, solve the following systems of equations by graphing. 333. {2xy=54x2y=10In the following exercises, solve the following systems of equations by graphing. 334. {x+2y=4y= 1 2x3In the following exercises, without graphing determine the number of solutions and then classify the system of equations. 335. {y= 2 5x+22x+5y=10In the following exercises, without graphing determine the number of solutions and then classify the system of equations. 336. {3x+2y=6y=3x+4In the following exercises, without graphing determine the number of solutions and then classify the system of equations. 337. {5x4y=0y= 5 4x5In the following exercises, without graphing determine the number of solutions and then classify the system of equations. 338. {y= 3 4x+16x+8y=8LaVelle is making a pitcher of caffe mocha. For each ounce of chocolate syrup, she uses five ounces of coffee. How many ounces of chocolate syrup and how many ounces of coffee does she need to make 48 ounces of caffe mocha?Eli is making a party mix that contains pretzels and chex. For each cup of pretzels, he uses three cups of chex. How many cups of pretzels and how many cups of chex does he need to make 12 cups of party mix?In the following exercises, solve the systems of equations by substitution. 341. {3xy=5y=2x+4In the following exercises, solve the systems of equations by substitution. 342. {3x2y=2y= 1 2x+3In the following exercises, solve the systems of equations by substitution. 343. {xy=02x+5y=14In the following exercises, solve the systems of equations by substitution. 344. {y=2x+7y= 2 3x1In the following exercises, solve the systems of equations by substitution. 345. {y=5x5x+y=6In the following exercises, solve the systems of equations by substitution. 346. {y= 1 3x+2x+3y=6In the following exercises, translate to a system of equations and solve. 347. The sum of two number is 55. One number is 11 less than the other. Find the numbers.In the following exercises, translate to a system of equations and solve. 348. The perimeter of a rectangle is 128. The length is 16 more than the width. Find the length and width.In the following exercises, translate to a system of equations and solve. 349. The measure of one of the small angles of a right triangle is 2 less than 3 times the measure of the other small angle. Find the measure of both angles.In the following exercises, translate to a system of equations and solve. 350. Gabriela works for an insurance company that pays her a salary of $32,000 plus a commission of $100 for each policy she sells. She is considering changing jobs to a company that would pay a salary of $40,000 plus a commission of $80 for each policy sold. How many policies would Gabriela need to sell to make the total pay the same?In the following exercises, solve the systems of equations by elimination. 351. {x+y=12xy=10In the following exercises, solve the systems of equations by elimination. 352. {4x+2y=24x3y=9In the following exercises, solve the systems of equations by elimination. 353. {3x8y=20x+3y=1In the following exercises, solve the systems of equations by elimination. 354. {3x2y=64x+3y=8In the following exercises, solve the systems of equations by elimination. 355. {9x+4y=25x+3y=5Solve a System of Equations by Elimination In the following exercises, solve the systems of equations by elimination. 356. {x+3y=82x6y=20In the following exercises, translate to a system of equations and solve. 357. The sum of two numbers is 90 . Their difference is 16. Find the numbers.In the following exercises, translate to a system of equations and solve. 358. Omar stops at a donut shop every day on his way to work. Last week he had 8 donuts and 5 cappuccinos, which gave him a total of 3,000 calories. This week he had 6 donuts and 3 cappuccinos, which was a total of 2,160 calories. How many calories are in one donut? How many calories are in one cappuccino?In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination. 359. {6x5y=273x+10y=24In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination. 360.{y=3x94x5y=23In the following exercises, translate to a system of equations. Do not solve the system. 361. The sum of two numbers is 32 . One number is two less thantwice the other. Find the numbers.In the following exercises, translate to a system of equations. Do not solve the system. 362. Four times a number plus three times a second number is 9 . Twice the first number plus the second number is three. Find the numbers.In the following exercises, translate to a system of equations. Do not solve the system. 363. Last month Jim and Debbie earned $7,200. Debbie earned $1,600 more than Jim earned. How much did they each earn?In the following exercises, translate to a system of equations. Do not solve the system. 364. Henri has $24,000 invested instocks and bonds. The amount instocks is $6,000 more than threetimes the amount in bonds. Howmuch is each investment?In the following exercises, translate to a system of equations and solve. 365. Pam is 3 years older than hersister, Jan. The sum of their ages is99. Find their ages.In the following exercises, translate to a system of equations and solve. 366. Mollie wants to plant 200bulbs in her garden. Shewantsallirises and tulips. She wants to plantthree times as many tulips as irises.How many irises and how manytulips should she plant?In the following exercises, translate to a system of equations and solve. 367. The difference of twosupplementary angles is 58degrees. Find the measures of theangles.In the following exercises, translate to a system of equations and solve. 368. Two angles are complementary. The measure of the larger angle is five more than four times the measure of the smaller angle. Find the measures of both angles.In the following exercises, translate to a system of equations and solve. 369. Becca is hanging a 28 foot floral garland on the two sides and top of a pergola to prepare for a wedding. The height is four feet less than the width. Find the height and width of the pergola.In the following exercises, translate to a system of equations and solve. 370. The perimeter of a city rectangular park is 1428 feet. The length is 78 feet more than twice the width. Find the length and width of the park.In the following exercises, translate to a system of equations and solve. 371. Sheila and Lenore were driving to their grandmother’s house. Lenore left one hour after Sheila. Sheila drove at a rate of 45 mph, and Lenore drove at a rate of60 mph. How long will it take for Lenore to catch up to Sheila?In the following exercises, translate to a system of equations and solve. 372. Bob left home, riding his bike at a rate of 10 miles per hour to go to the lake. Cheryl, his wife, left 45 minutes (34hour) later, driving her car at a rate of 25 miles per hour. How long will it take Cheryl to catch up to Bob?In the following exercises, translate to a system of equations and solve. 373. Marcus can drive his boat 36 miles down the river in three hours but takes four hours to return upstream. Find the rate of the boat in still water and the rate of the current.In the following exercises, translate to a system of equations and solve. 374. A passenger jet can fly 804 miles in 2 hours with a tailwind but only 776 miles in 2 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.In the following exercises, translate to a system of equations and solve. 375. Lynn paid a total of $2,780 for 261 tickets to the theater. Student tickets cost $10 and adult tickets cost $15. How many student tickets and how many adult tickets didLynn buy?In the following exercises, translate to a system of equations and solve. 376. Priam has dimes and pennies in a cup holder in his car. The total value of the coins is $4.21. The number of dimes is three less than four times the number of pennies. How many dimes and how many pennies are in the cup?In the following exercises, translate to a system of equations and solve. 377. Yumi wants to make 12 cups of party mix using candies and nuts. Her budget requires the party mix to cost her $1.29 per cup. The candies are $2.49 per cup and the nuts are $0.69 per cup. How many cups of candies and how many cups of nuts should she use?In the following exercises, translate to a system of equations and solve. 378. A scientist needs 70 liters of a 40% solution of alcohol. He has a 30% and a 60% solution available. How many liters of the 30% and how many liters of the 60% solutions should he mix to make the 40% solution?In the following exercises, translate to a system of equations and solve. 379. Jack has $12,000 to invest and wants to earn 7.5% interest per year. He will put some of the money into a savings account thatearns 4% per year and the rest into CD account that earns 9% per year. How much money should he put into each account?In the following exercises, translate to a system of equations and solve. 380. When she graduates college, Linda will owe $43,000 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owes for one year was $1585. What is the amount of each loan?In the following exercises, determine whether each ordered pair is a solution to the system. 381. {4x+y63xy12 (a) (2,1) (b) (3,2)In the following exercises, determine whether each ordered pair is a solution to the system. 382. {y 1 3x+2x 1 4y10 (a) (6,5) (b) (15,8)In the following exercises, solve each system by graphing. 383. {y3x+1yx2In the following exercises, solve each system by graphing. 384. {xy1y 1 3x2In the following exercises, solve each system by graphing. 385. {2x3y63x+4y12In the following exercises, solve each system by graphing. 386. {y 3 4x+1x5In the following exercises, solve each system by graphing. 387. {x+3y5y 1 3x+6In the following exercises, solve each system by graphing. 388. {y2x56x+3y4In the following exercises, translate to a system of inequalities and solve. 389. Roxana makes bracelets and necklaces and sells them at the farmers’ market. She sells the bracelets for $12 each and the necklaces for $18 each. At the market next weekend she will have room to display no more than 40 pieces, and she needs to sell at least $500 worth in order to earn a profit. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Should she display 26 bracelets and 14 necklaces? (d) Should she display 39 bracelets and 1 necklace?In the following exercises, translate to a system of inequalities and solve. 390. Annie has a budget of $600 to purchase paperback books and hardcover books for her classroom. She wants the number of hardcover to be at least 5 more than three times the number of paperback books. Paperback books cost $4 each and hardcover books cost $15 each. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Can she buy 10 paperback books and 37 hardcover books?{x4y=82x+5y=10 (a) (0,2) (b)(4,3)In the following exercises, solve the following systems by graphing. 392. {xy=5x+2y=4In the following exercises, solve the following systems by graphing. 393. {xy2y3x+1In the following exercises, solve each system of equations. Use either substitution or elimination. 394. {3x2y=3y=2x1In the following exercises, solve each system of equations. Use either substitution or elimination. 395. {x+y=3xy=11In the following exercises, solve each system of equations. Use either substitution or elimination. 396. {4x3y=75x2y=0In the following exercises, solve each system of equations. Use either substitution or elimination. 397. {y= 4 5x+18x+10y=10In the following exercises, solve each system of equations. Use either substitution or elimination. 398. {2x+3y=124x+6y=16In the following exercises, translate to a system of equations and solve. 399. The sum of two numbers is 24 . One number is 104 less than the other. Find the numbers.In the following exercises, translate to a system of equations and solve. 400. Ramon wants to plant cucumbers and tomatoes in his garden. He has room for 16 plants, and he wants to plant three times as many cucumbers as tomatoes. How many cucumbers and how many tomatoes should he plant?In the following exercises, translate to a system of equations and solve. 401. Two angles are complementary. The measure of the larger angle is six more than twice the measure of the smaller angle. Find the measures of both angles.In the following exercises, translate to a system of equations and solve. 402. On Monday, Lance ran for 30 minutes and swam for 20 minutes. His fitness app told him he had burned 610 calories. On Wednesday, the fitness app told him he burned 695 calories when he ran for 25 minutes and swam for 40 minutes. How many calories did he burn for one minute of running? How many calories did he burn for one minute of swimming?In the following exercises, translate to a system of equations and solve. 403. Kathy left home to walk to the mall, walking quickly at a rate of 4 miles per hour. Her sister Abby left home 15 minutes later and rode her bike to the mall at a rate of 10 miles per hour. How long will it take Abby to catch up to Kathy?In the following exercises, translate to a system of equations and solve. 404. It takes 512 hours for a jet to fly 2,475 miles with a headwind from San Jose, California to Lihue, Hawaii. The return flight from Lihue to San Jose with a tailwind, takes 5 hours. Find the speed of the jet in still air and the speed of the wind.In the following exercises, translate to a system of equations and solve. 405. Liz paid $160 for 28 tickets to take the Brownie troop to the science museum. Children’s tickets cost $5 and adult tickets cost $9. How many children’s tickets and how many adult tickets did Liz buy?In the following exercises, translate to a system of equations and solve. 406. A pharmacist needs 20 liters of a 2% saline solution. He has a 1% and a 5% solution available. How many liters of the 1% and how many liters of the 5% solutions should she mix to make the 2% solution?In the following exercises, translate to a system of equations and solve. 407. Translate to a system of inequalities and solve. Andi wants to spend no more than $50 on Halloween treats. She wants to buy candy bars that cost $1 each and lollipops that cost $0.50 each, and she wants the number of lollipops to be at least three times the number of candy bars. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Can she buy 20 candy bars and 70 lollipops? (d) Can she buy 15 candy bars and 65 lollipops?Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial: (a) 5b (b) 8y37y2y3 (c) 3x25x+9 (d) 814a2 (e) 5x6Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial: (a) 27z38 (b) 12m35m22m (c) 56 (d) 8x47x26x5 (e) n4Find the degree of the following polynomials: (a) 15b (b) 10z4+4z25 (c) 12c5d4+9c3d97 (d) 3x2y4x (e) 9Find the degree of the following polynomials: (a) 52 (b) a4b17a4 (c) 5x+6y+2z (d) 3x25x+7 (e) a3Add: 12q2+9q2 .Add: 15c2+8c2 .Subtract: 8m(5m) .Subtract: 15z3(5z3) .Add: 8y2+3z23y2 .Add: 3m2+n27m2 .Simplify: m2n28m2+4n2 .Simplify: pq26p5q2 .Find the sum: (7x24x+5)+(x27x+3) .Find the sum: (14y2+6y4)+(3y2+8y+5) .Find the difference: (8x2+3x19)(7x214) .Find the difference: (9b25b4)(3b25b7) .Subtract: (5z26z2) from (7z2+6z4) .Subtract: (x25x8) from (6x2+9x1) .Find the sum: (3x24xy+5y2)+(2x2xy) .Find the sum: (2x23xy2y2)+(5x23xy) .Find the difference: (a2+b2)(a2+5ab6b2) .Find the difference: (m2+n2)(m27mn3n2) .Simplify: (x3x2y)(xy2+y)+(x2y+xy2) .Simplify: (p3p2q)(pq2+q3)(p2q+pq2) .Evaluate: 3x2+2x15 when (a)x=3 (b)x=5 (c)x=0Evaluate: 5z2z4 when (a) z=2 (b) z=0 (c) z=2The polynomial 16t2+250 gives the height of a ball t seconds after it is dropped from a 250-foot tall building. Find the height after t=0 seconds.The polynomial 16t2+250 gives the height of a ball t seconds after it is dropped from a 250-foot tall building. Find the height after t=3 seconds.The polynomial 6x2+15xy gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side x feet and sides of height y feet. Find the cost of producing a box with x=6 feet and y=4 feet.The polynomial 6x2+15xy gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side x feet and sides of height y feet. Find the cost of producing a box with x=5 feet and y=8 feet.In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial. 1. (a) 81b524b3+1 (b) 5c3+11c2c8 (c) 1415y+17 (d) 5 (e) 4y+17In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial. 2. (a) x2y2 (b) 13c4 (c) x2+5x7 (d) x2y22xy+8 (e) 19In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial. 3. (a) 83x (b) z25z6 (c) y38y2+2y16 (d) 81b524b3+1 (e) 18In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial. 3. (a) 11y2 (b) 73 (c) 6x23xy+4x2y+y2 (d) 4y+14 (e) 5c3+11c2c8In the following exercises, determine the degree of each polynomial. 5. (a) 6a2+12a+14 (b) 18xy2z (c) 5x+2 (d) y38y2+2y16 (e) -24In the following exercises, determine the degree of each polynomial. 6. (a) 9y310y2+2y6 (b) 12p4 (c) a2+9a+18 (d) 20x2y210a2b2+30 (e) 17In the following exercises, determine the degree of each polynomial. 7. (a) 1429x (b) z25z6 (c) y38y2+2y16 (d) 23ab214 (e) -3In the following exercises, determine the degree of each polynomial. 8. (a) 62y2 (b) 15 (c) 6x23xy+4x2y+y2 (d) 109x (e) m4+4m3+6m2+1In the following exercises, add or subtract the monomials. 9. 7x2+5x2In the following exercises, add or subtract the monomials. 10. 4y3+6y3In the following exercises, add or subtract the monomials. 11. 12w+18wIn the following exercises, add or subtract the monomials. 12. 3m+9mIn the following exercises, add or subtract the monomials. 13. 4a9aIn the following exercises, add or subtract the monomials. 14. y5yIn the following exercises, add or subtract the monomials. 15. 28x(12x)In the following exercises, add or subtract the monomials. 16. 13z(4z)In the following exercises, add or subtract the monomials. 17. 5b17bIn the following exercises, add or subtract the monomials. 18. 10x35xIn the following exercises, add or subtract the monomials. 19. 12a+5b22aIn the following exercises, add or subtract the monomials. 20. 14x3y13xIn the following exercises, add or subtract the monomials. 21. 2a2+b26a2In the following exercises, add or subtract the monomials. 22. 5u2+4v26u2In the following exercises, add or subtract the monomials. 23. xy25x5y2In the following exercises, add or subtract the monomials. 24. pq24p3q2In the following exercises, add or subtract the monomials. 25. a2b4a5ab2In the following exercises, add or subtract the monomials. 26. x2y3x+7xy2In the following exercises, add or subtract the monomials. 27. 12a+8bIn the following exercises, add or subtract the monomials. 28. 19y+5zIn the following exercises, add or subtract the monomials. 29. Add: 4a,3b,8aIn the following exercises, add or subtract the monomials. 30. Add: 4x,3y,3xIn the following exercises, add or subtract the monomials. 31. Subtract 5x6 from 12x6 .In the following exercises, add or subtract the monomials. 32. Subtract 2p4 from 7p4 .In the following exercises, add or subtract the polynomials. 33. (5y2+12y+4)+(6y28y+7)In the following exercises, add or subtract the polynomials. 34. (4y2+10y+3)+(8y26y+5)In the following exercises, add or subtract the polynomials. 35. (x2+6x+8)+(4x2+11x9)In the following exercises, add or subtract the polynomials. 36. (y2+9y+4)+(2y25y1)In the following exercises, add or subtract the polynomials. 37. (8x25x+2)+(3x2+3)In the following exercises, add or subtract the polynomials. 38. (7x29x+2)+(6x24)In the following exercises, add or subtract the polynomials. 39. (5a2+8)+(a24a9)In the following exercises, add or subtract the polynomials. 40. (p26p18)+(2p2+11)In the following exercises, add or subtract the polynomials. 41. (4m26m3)(2m2+m7)In the following exercises, add or subtract the polynomials. 42. (3b24b+1)(5b2b2)In the following exercises, add or subtract the polynomials. 43. (a2+8a+5)(a23a+2)In the following exercises, add or subtract the polynomials. 44. (b27b+5)(b22b+9)In the following exercises, add or subtract the polynomials. 45. (12s215s)(s9)In the following exercises, add or subtract the polynomials. 46. (10r220r)(r8)In the following exercises, add or subtract the polynomials. 47. Subtract (9x2+2) from (12x3x+6) .In the following exercises, add or subtract the polynomials. 48. Subtract (5y2y+12) from (10y28y20) .In the following exercises, add or subtract the polynomials. 49. Subtract (7w24w+2) from (8w2w+6) .In the following exercises, add or subtract the polynomials. 50. Subtract (5x2x+12) from (9x26x20) .In the following exercises, add or subtract the polynomials. 51. Find the sum of (2p38) and (p2+9p+18) .In the following exercises, add or subtract the polynomials. 52. Find the sum of (q2+4q+13) and (7q33) .In the following exercises, add or subtract the polynomials. 53. Find the sum of (8a38a) and (a2+6a+12) .In the following exercises, add or subtract the polynomials. 54. Find the sum of (b2+5b+13) and (4b36) .In the following exercises, add or subtract the polynomials. 55. Find the difference of (w2+w42) and (w210w+24) .In the following exercises, add or subtract the polynomials. 56. Find the difference of (z23z18) and (z2+5z20) .In the following exercises, add or subtract the polynomials. 57. Find the difference of (c2+4c33) and (c28c+12) .In the following exercises, add or subtract the polynomials. 58. Find the difference of (t25t15) and (t2+4t17) .In the following exercises, add or subtract the polynomials. 59. (7x22xy+6y2)+(3x25xy)In the following exercises, add or subtract the polynomials. 60. (5x24xy3y2)+(2x27xy)In the following exercises, add or subtract the polynomials. 61. (7m2+mn8n2)+(3m2+2mn)In the following exercises, add or subtract the polynomials. 62. (2r23rs2s2)+(5r23rs)In the following exercises, add or subtract the polynomials. 63. (a2b2)(a2+3ab4b2)