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Bartleby Sitemap - Textbook Solutions

All Textbook Solutions for Intermediate Algebra

Solve the system by graphing: {y=3x16x2y=6 .Solve the system by graphing: {y=3x66x+2y=12 .Solve the system by graphing: {y=12x42x4y=16 .Without graphing, determine the number of solutions and then classify the system of equations. (a) {y=2x44x+2y=9 (b) {3x+2y=22x+y=1 Without graphing, determine the number of solutions and then classify the system of equations. (a) {y=13x5x3y=6 (b) {x+4y=12x+y=3 Solve the system by substitution: {2x+y=11x+3y=9 .Solve the system by substitution: {2x+y=14x+3y=3 .Solve the system by substitution: {x4y=43x+4y=0 .Solve the system by substitution: {4xy=02x3y=5 .Solve the system by elimination: {3x+y=52x3y=7 .Solve the system by elimination: {4x+y=52x2y=2 .Solve the system by elimination: {3x4y=95x+3y=14 .Solve the system by elimination: {7x+8y=43x5y=27 .Solve the system by elimination: {13x12y=134xy=52 .Solve the system by elimination: {x+35y=1512x23y=56 .Solve the system by elimination: {5x3y=15y=5+53x .Solve the system by elimination: {x+2y=6y=12x+3 .For each system of linear equations decide whether it would be more convenient to solve it by substitution or elimination. Explain your answer. (a) {4x5y=323x+2y=1 (b) {x=2y13x5y=7 For each system of linear equations decide whether it would be more convenient to solve it by substitution or elimination. Explain your answer. (a) {y=2x13x4y=6 (b) {6x2y=123x+7y=13 In the following exercises, determine if the following points are solutions to the given system of equations. 1. {2x6y=03x4y=5 (a) (3,1) (b) (3,4)In the following exercises, determine if the following points are solutions to the given system of equations. 2. {3x+y=8x+2y=9 (a) (5,7) (b) (5,7)In the following exercises, determine if the following points are solutions to the given system of equations. 3. {x+y=2y= 3 4x (a) (87,67) (b) (1,34)In the following exercises, determine if the following points are solutions to the given system of equations. 4. {2x+3y=6y= 2 3x+2 (a) (6,2) (b) (3,4)In the following exercises, solve the following systems of equations by graphing. 5. {3x+y=32x+3y=5 In the following exercises, solve the following systems of equations by graphing. 6. {x+y=22x+y=4 In the following exercises, solve the following systems of equations by graphing. 7. {y=x+2y=2x+2 In the following exercises, solve the following systems of equations by graphing. 8. {y=x2y=3x+2 In the following exercises, solve the following systems of equations by graphing. 9. {y= 3 2x+1y= 1 2x+5 In the following exercises, solve the following systems of equations by graphing. 10. {y= 2 3x2y= 1 3x5 In the following exercises, solve the following systems of equations by graphing. 11. {x+y=4x+2y=2 In the following exercises, solve the following systems of equations by graphing. 12. {x+3y=3x+3y=3 In the following exercises, solve the following systems of equations by graphing. 13. {2x+3y=3x+3y=12 In the following exercises, solve the following systems of equations by graphing. 14. {2xy=42x+3y=12 In the following exercises, solve the following systems of equations by graphing. 15. {x+3y=6y= 4 3x+4 In the following exercises, solve the following systems of equations by graphing. 16. {x+2y=6y= 1 2x1 In the following exercises, solve the following systems of equations by graphing. 17. {2x+4y=4y= 1 2x In the following exercises, solve the following systems of equations by graphing. 18. {3x+5y=10y= 3 5x+1 In the following exercises, solve the following systems of equations by graphing. 19. {4x3y=88x6y=14 In the following exercises, solve the following systems of equations by graphing. 20. {x+3y=42x6y=3 In the following exercises, solve the following systems of equations by graphing. 21. {x=3y+42x+6y=8 In the following exercises, solve the following systems of equations by graphing. 22. {4x=3y+78x6y=14 In the following exercises, solve the following systems of equations by graphing. 23. {2x+y=68x4y=24 In the following exercises, solve the following systems of equations by graphing. 24. {5x+2y=710x4y=14 Without graphing, determine the number of solutions and then classify the system of equations. 25. {y= 2 3x+12x+3y=5 Without graphing, determine the number of solutions and then classify the system of equations. 26. {y= 3 2x+12x3y=7 Without graphing, determine the number of solutions and then classify the system of equations. 27. {5x+3y=42x3y=5 Without graphing, determine the number of solutions and then classify the system of equations. 28. {y= 1 2x+5x+2y=10 Without graphing, determine the number of solutions and then classify the system of equations. 29. {5x2y=10y= 5 2x5 In the following exercises, solve the systems of equations by substitution. 30. {2x+y=43x2y=6 In the following exercises, solve the systems of equations by substitution. 31. {2x+y=23xy=7 In the following exercises, solve the systems of equations by substitution. 32. {x2y=52x3y=4 In the following exercises, solve the systems of equations by substitution. 33. {x3y=92x+5y=4 In the following exercises, solve the systems of equations by substitution. 34. {5x2y=6y=3x+3 In the following exercises, solve the systems of equations by substitution. 35. {2x+2y=6y=3x+1 In the following exercises, solve the systems of equations by substitution. 36. {2x+5y=1y= 1 3x2 In the following exercises, solve the systems of equations by substitution. 37. {3x+4y=1y= 2 5x+2 In the following exercises, solve the systems of equations by substitution. 38.{2x+y=5x2y=15 In the following exercises, solve the systems of equations by substitution. 39. {4x+y=10x2y=20 In the following exercises, solve the systems of equations by substitution. 40. {y=2x1y= 1 3x+4 In the following exercises, solve the systems of equations by substitution. 41. {y=x6y= 3 2x+4 In the following exercises, solve the systems of equations by substitution. 42. {x=2y4x8y=0 In the following exercises, solve the systems of equations by substitution. 43. {2x16y=8x8y=4 In the following exercises, solve the systems of equations by substitution. 44. {y= 7 8x+47x+8y=6 In the following exercises, solve the systems of equations by substitution. 45. {y= 2 3x+52x+3y=11 In the following exercises, solve the systems of equations by elimination. 46. {5x+2y=23xy=0 In the following exercises, solve the systems of equations by elimination. 47. {6x5y=12x+y=13 In the following exercises, solve the systems of equations by elimination. 48. {2x5y=73xy=17 In the following exercises, solve the systems of equations by elimination. 49. {5x3y=12xy=2 In the following exercises, solve the systems of equations by elimination. 50. {3x5y=95x+2y=16 In the following exercises, solve the systems of equations by elimination. 51. {4x3y=32x+5y=31 In the following exercises, solve the systems of equations by elimination. 52. {3x+8y=32x+5y=3 In the following exercises, solve the systems of equations by elimination. 53. {11x+9y=57x+5y=1 In the following exercises, solve the systems of equations by elimination. 54. {3x+8y=675x+3y=60 In the following exercises, solve the systems of equations by elimination. 55. {2x+9y=43x+13y=7 In the following exercises, solve the systems of equations by elimination. 56. { 1 3xy=3x+ 5 2y=2 In the following exercises, solve the systems of equations by elimination. 57. {x+ 1 2y= 3 2 1 5x 1 5y=3 In the following exercises, solve the systems of equations by elimination. 58. {x+ 1 3y=1 1 3x+ 1 2y=1 In the following exercises, solve the systems of equations by elimination. 59.{ 1 3xy=3 2 3x+ 5 2y=3 In the following exercises, solve the systems of equations by elimination. 60.{2x+y=36x+3y=9 In the following exercises, solve the systems of equations by elimination. 61. {x4y=13x+12y=3 In the following exercises, solve the systems of equations by elimination. 62. {3xy=86x+2y=16 In the following exercises, solve the systems of equations by elimination. 63. {4x+3y=220x+15y=10 In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination. 64. (a) {8x15y=326x+3y=5 (b) {x=4y34x2y=6 In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination. 65. (a) {y=7x53x2y=16 (b) {12x5y=423x+7y=15 In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination. 66. (a) {y=4x+95x2y=21 (b) {9x4y=243x+5y=14 In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination. 67. (a) {14x15y=307x+2y=10 (b) {x=9y112x7y=27 In a system of linear equations, the two equations have the same intercepts. Describe the possible solutions to the system.Solve the system of equations by substitution and explain all your steps in words: {3x+y=12x=y8 .Solve the system of equations by elimination and explain all your steps in words: {5x+4y=102x=3y+27 .Solve the system of equations {x+y=10xy=6 (a) by graphing (b) by substitution (c) Which method do you prefer? Why?The sum of two numbers is 10. One number is 4 less than the other. Find the numbers.The sum of two numbers is 6 . One number is 10 less than the other. Find the numbers.Geraldine has been offered positions by two insurance companies. The first company pays a salary of $12,000 plus a commission of $100 for each policy sold. The second pays a salary of $20,000 plus a commission of $50 for each policy sold. How many policies would need to be sold to make the total pay the same?Kenneth currently sells suits for company A at a salary of $22,000 plus a $10 commission for each suit sold. Company B offers him a position with a salary of $28,000 plus a $4 commission for each suit sold. How many suits would Kenneth need to sell for the options to be equal?Translate to a system of equations and then solve: Mark went to the gym and did 40 minutes of Bikram hot yoga and 10 minutes of jumping jacks. He burned 510 calories. The next time he went to the gym, he did 30 minutes of Bikram hot yoga and 20 minutes of jumping jacks burning 470 calories. How many calories were burned for each minute of yoga? How many calories were burned for each minute of jumping jacks?Translate to a system of equations and then solve: Erin spent 30 minutes on the rowing machine and 20 minutes lifting weights at the gym and burned 430 calories. During her next visit to the gym she spent 50 minutes on the rowing machine and 10 minutes lifting weights and burned 600 calories. How many calories did she burn for each minutes on the rowing machine? How many calories did she burn for each minute of weight lifting?Translate to a system of equations and then solve: The difference of two complementary angles is 20 degrees. Find the measures of the angles.Translate to a system of equations and then solve: The difference of two complementary angles is 80 degrees. Find the measures of the angles.Translate to a system of equations and then solve: Two angles are supplementary. The measure of the larger angle is 12 degrees more than three times the smaller angle. Find the measures of the angles.Translate to a system of equations and then solve: Two angles are supplementary. The measure of the larger angle is 18 less than twice the measure of the smaller angle. Find the measures of the angles.The measure of one of the small angles of a right triangle is 2 more than 3 times the measure of the other small angle. Find the measure of both angles.The measure of one of the small angles of a right triangle is 18 less than twice the measure of the other small angle. Find the measure of both angles.Translate to a system of equations and then solve: Mario wants to put a fence around the pool in his backyard. Since one side is adjacent to the house, he will only need to fence three sides. There are two long sides and the one shorter side is parallel to the house. He needs 155 feet of fencing to enclose the pool. The length of the long side is 10 feet less than twice the width. Find the length and width of the pool area to be enclosed.Translate to a system of equations and then solve: Alexis wants to build a rectangular dog run in her yard adjacent to her neighbor’s fence. She will use 136 feet of fencing to completely enclose the rectangular dog run. The length of the dog run along the neighbor’s fence will be 16 feet less than twice the width. Find the length and width of the dog run.Translate to a system of equations and then solve: Mitchell left Detroit on the interstate driving south towards Orlando at a speed of 60 miles per hour. Clark left Detroit 1 hour later traveling at a speed of 75 miles per hour, following the same route as Mitchell. How long will it take Clark to catch Mitchell?Translate to a system of equations and then solve: Charlie left his mother’s house traveling at an average speed of 36 miles per hour. His sister Sally left 15 minutes ( 14 hour) later traveling the same route at an average speed of 42 miles per hour. How long before Sally catches up to Charlie?Translate to a system of equations and then solve: A Mississippi river boat cruise sailed 120 miles upstream for 12 hours and then took 10 hours to return to the dock. Find the speed of the river boat in still water and the speed of the river current.Translate to a system of equations and then solve: Jason paddled his canoe 24 miles upstream for 4 hours. It took him 3 hours to paddle back. Find the speed of the canoe in still water and the speed of the river current.Translate to a system of equations and then solve: A small jet can fly 1,325 miles in 5 hours with a tailwind but only 1,035 miles in 5 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.Translate to a system of equations and then solve: A commercial jet can fly 1,728 miles in 4 hours with a tailwind but only 1,536 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. 72. The sum of two number is 15. One number is 3 less than the other. Find the numbers.In the following exercises, translate to a system of equations and solve. 73. The sum of two number is 30. One number is 4 less than the other. Find the numbers.In the following exercises, translate to a system of equations and solve. 74. The sum of two number is -16. One number is 20 less than the other. Find the numbers.In the following exercises, translate to a system of equations and solve. 75. The sum of two number is 26 . One number is 12 less than the other. Find the numbers.In the following exercises, translate to a system of equations and solve. 76. The sum of two numbers is 65. Their difference is 25. Find the numbers.In the following exercises, translate to a system of equations and solve. 77. The sum of two numbers is 37. Their difference is 9. Find the numbers.In the following exercises, translate to a system of equations and solve. 78. The sum of two numbers is 27 . Their difference is 59 . Find the numbers.In the following exercises, translate to a system of equations and solve. 79. The sum of two numbers is 45 . Their difference is 89 . Find the numbers.In the following exercises, translate to a system of equations and solve. 80. Maxim has been offered positions by two car companies. The first company pays a salary of $10,000 plus a commission of $1000 for each car sold. The second pays a salary of $20,000 plus a commission of $500 for each car sold. How many cars would need to be sold to make the total pay the same?In the following exercises, translate to a system of equations and solve. 81. Jackie has been offered positions by two cable companies. The first company pays a salary of $14,000 plus a commission of $100 for each cable package sold. The second pays a salary of $20,000 plus a commission of $25 for each cable package sold. How many cable packages would need to be sold to make the total pay the same?In the following exercises, translate to a system of equations and solve. 82. Amara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a $20 commission for each television she sells. How televisions would Amara need to sell for the options to be equal?In the following exercises, translate to a system of equations and solve. 83. Mitchell currently sells stoves for company A at a salary of $12,000 plus a $150 commission for each stove he sells. Company B offers him a position with a salary of $24,000 plus a $50 commission for each stove he sells. How many stoves would Mitchell need to sell for the options to be equal?In the following exercises, translate to a system of equations and solve. 84. Two containers of gasoline hold a total of fifty gallons. The big container can hold ten gallons less than twice the small container. How many gallons does each container hold?In the following exercises, translate to a system of equations and solve. 85. June needs 48 gallons of punch for a party and has two different coolers to carry it in. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold?In the following exercises, translate to a system of equations and solve. 86. Shelly spent 10 minutes jogging and 20 minutes cycling and burned 300 calories. The next day, Shelly swapped times, doing 20 minutes of jogging and 10 minutes of cycling and burned the same number of calories. How many calories were burned for each minute of jogging and how many for each minute of cycling?In the following exercises, translate to a system of equations and solve. 87. Drew burned 1800 calories Friday playing one hour of basketball and canoeing for two hours. Saturday he spent two hours playing basketball and three hours canoeing and burned 3200 calories. How many calories did he burn per hour when playing basketball? How many calories did he burn per hour when canoeing?In the following exercises, translate to a system of equations and solve. 88. Troy and Lisa were shopping for school supplies. Each purchased different quantities of the same notebook and thumb drive. Troy bought four notebooks and five thumb drives for $116. Lisa bought two notebooks and three thumb dives for $68. Find the cost of each notebook and each thumb drive.In the following exercises, translate to a system of equations and solve. 89. Nancy bought seven pounds of oranges and three pounds of bananas for $17. Her husband later bought three pounds of oranges and six pounds of bananas for $12. What was the cost per pound of the oranges and the bananas?In the following exercises, translate to a system of equations and solve. 90. Andrea is buying some new shirts and sweaters. She is able to buy 3 shirts and 2 sweaters for $114 or she is able to buy 2 shirts and 4 sweaters for $164. How much does a shirt cost? How much does a sweater cost?In the following exercises, translate to a system of equations and solve. 91. Peter is buying office supplies. He is able to buy 3 packages ofpaper and 4 staplers for $40 or he is able to buy 5 packages of paper and 6 staplers for $62. How much does a package of paper cost? How much does a stapler cost?In the following exercises, translate to a system of equations and solve. 92. The total amount of sodium in 2 hot dogs and 3 cups of cottage cheese is 4720 mg. The total amount of sodium in 5 hot dogs and 2 cups of cottage cheese is 6300 mg. How much sodium is in a hot dog? How much sodium is in a cup of cottage cheese?In the following exercises, translate to a system of equations and solve. 93. The total number of calories in 2 hot dogs and 3 cups of cottage cheese is 960 calories. The total number of calories in 5 hot dogs and 2 cups of cottage cheese is 1190 calories. How many calories are in a hot dog? How many calories are in a cup of cottage cheese?In the following exercises, translate to a system of equations and solve. 94. Molly is making strawberry infused water. For each ounce of strawberry juice, she uses three times as many ounces of water as juice. How many ounces of strawberry juice and how many ounces of water does she need to make 64 ounces of strawberry infused water?In the following exercises, translate to a system of equations and solve. 95. Owen is making lemonade from concentrate. The number of quarts of water he needs is 4 times the number of quarts of concentrate. How many quarts of water and how many quarts of concentrate does Owen need to make 100 quarts of lemonade?In the following exercises, translate to a system of equations and solve. 96. The difference of two complementary angles is 55 degrees. Find the measures of the angles.In the following exercises, translate to a system of equations and solve. 97. The difference of two complementary angles is 17 degrees. Find the measures of the angles.In the following exercises, translate to a system of equations and solve. 98. Two angles are complementary. The measure of the larger angle is twelve less 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. 99. Two angles are complementary. The measure of the larger angle is ten 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. 100. The difference of two supplementary angles is 8 degrees. Find the measures of the angles.In the following exercises, translate to a system of equations and solve. 101. The difference of two supplementary angles is 88 degrees. Find the measures of the angles.In the following exercises, translate to a system of equations and solve. 102. Two angles are supplementary. The measure of the larger angle is four more than three 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. 103. Two angles are supplementary. The measure of the larger angle is five less 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. 104. The measure of one of the small angles of a right triangle is 14 more 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. 105. The measure of one of the small angles of a right triangle is 26 more 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. 106. The measure of one of the small angles of a right triangle is 15 less than twice 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. 107. The measure of one of the small angles of a right triangle is 45 less than twice 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. 108. Wayne is hanging a string of lights 45 feet long around the three sides of his patio, which is adjacent to his house. The length of his patio, the side along the house, is five feet longer than twice its width. Find the length and width of the patio.In the following exercises, translate to a system of equations and solve. 109. Darrin is hanging 200 feet of Christmas garland on the three sides of fencing that enclose his front yard. The length is five feet less than three times the width. Find the length and width of the fencing.In the following exercises, translate to a system of equations and solve. 110. A frame around a family portrait has a perimeter of 90 inches. The length is fifteen less than twice the width. Find the length and width of the frame.In the following exercises, translate to a system of equations and solve. 111. The perimeter of a toddler play area is 100 feet. The length is ten more than three times the width. Find the length and widthof the play area.In the following exercises, translate to a system of equations and solve. 112. Sarah left Minneapolis heading east on the interstate at a speed of 60 mph. Her sister followed her on the same route, leaving two hours later and driving at a rate of 70 mph. How long will it take for Sarah’s sister to catch up to Sarah?In the following exercises, translate to a system of equations and solve. 113. College roommates John and David were driving home to the same town for the holidays. John drove 55 mph, and David, who left an hour later, drove 60 mph. How long will it take for David to catch up to John?In the following exercises, translate to a system of equations and solve. 114. At the end of spring break, Lucy left the beach and drove back towards home, driving at a rate of 40 mph. Lucy’s friend left the beach for home 30 minutes (half an hour) later, and drove 50 mph. How long did it take Lucy’s friend to catch up to Lucy?In the following exercises, translate to a system of equations and solve. 115. Felecia left her home to visit her daughter driving 45 mph. Her husband waited for the dog sitter to arrive and left home twenty minutes (1/3 hour) later. He drove 55 mph to catch up to Felecia. How long before he reaches her?In the following exercises, translate to a system of equations and solve. 116. The Jones family took a 12-mile canoe ride down the Indian River in two hours. After lunch, the return trip back up the river took three hours. Find the rate of the canoe in still water and the rate of the current.In the following exercises, translate to a system of equations and solve. 117. A motor boat travels 60 miles down a river in three hours but takes five 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. 118. 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. 119. 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.In the following exercises, translate to a system of equations and solve. 120. A small jet can fly 1072 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. 121. A small jet can fly 1435 miles in 5 hours with a tailwind but only 1,215 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. 122. 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. 123. A commercial jet can fly 1,320 miles in 3 hours with a tailwind but only 1170 miles in 3 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.Write an application problem similar to Example 4.14. Then translate to a system of equations and solve it.Write a uniform motion problem similar to Example 4.15 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: The box office at a movie theater sold 147 tickets for the evening show, and receipts totaled $1,302. How many $11 adult and how many $8 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: Priam has a collection of nickels and quarters, with a total value of $7.30. The number of nickels is six less than three times the number of quarters. How many nickels and how many quarters does he 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 $7000 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?The manufacturer of a weight training bench spends $15 to build each bench and sells them for $32. The manufacturer also has fixed costs each month of $25,500. (a) Find the cost function C when x benches are manufactured. (b) Find the revenue function R when x benches are sold. (c) Show the break-even point by graphing both the Revenue and Cost functions on the same grid. (d) Find the break-even point. Interpret what the break-even point means.The manufacturer of a weight training bench spends $120 to build each bench and sells them for $170. The manufacturer also has fixed costs each month of $150,000. (a) Find the cost function C when x benches are manufactured. (b) Find the revenue function R when x benches are sold. (c) Show the break-even point by graphing both the Revenue and Cost functions on the same grid. (d) Find the break-even point. Interpret what the break-even point means.In the following exercises, translate to a system of equations and solve. 126. 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. 127. Tickets for the Cirque du Soleil 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. 128. Tickets for an Amtrak train cost $10 for children and $22 for adults. Josie paid $1200 for a total of 72 tickets. How many children tickets and how many adult tickets did Josie buy?In the following exercises, translate to a system of equations and solve. 129. Tickets for a Minnesota Twins baseball game are $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. 130. Tickets for a dance recital cost $15 for adults and $7 dollars for children. The dance company sold 253 tickets and the total receipts were $2771. How many adult tickets and how many child tickets were sold?In the following exercises, translate to a system of equations and solve. 131. 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 $2204. How many adult tickets and how many child tickets were sold?In the following exercises, translate to a system of equations and solve. 132. 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. 133. 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. 134. Peter has been saving his loose change for several days. When he counted his quarters and nickels, 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. 135. Lucinda had a pocketful of dimes and quarters with a value of $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. 136. 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. 137. 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. 138. 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. 139. 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. 140. 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. 141. Joseph would like to make twelve pounds of a coffee blend at a cost of $6 per pound. He blends Ground Chicory at $5 a pound with Jamaican Blue Mountain at $9 per pound. How much of each type of coffee should he use?In the following exercises, translate to a system of equations and solve. 142. 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 twenty 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. 143. Twelve-year old Melody wants to sell bags of mixed candy at her lemonade stand. She will mix M&M’s that cost $4.89 per bag and Reese’s 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 M&M’s and how many bags of Reese’s Pieces should she use?In the following exercises, translate to a system of equations and solve. 144. Jotham needs 70 liters of a 50% solution of an 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. 145. 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. 146. 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. 147. 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. 148. 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. 149. A 90% antifreeze solution is to be mixed with a 75% antifreeze solution to get 360 liters of an 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. 150. Hattie had $3000 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. 151. Carol invested $2560 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. 152. Sam invested $48,000, some at 6% interest and the rest at 10%. How much did he invest at each rate if he received $4000 in interest in one year?In the following exercises, translate to a system of equations and solve. 153. 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 $4500 in interest in one year?In the following exercises, translate to a system of equations and solve. 154. 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 owes for one year was $2878.50. What is the amount of each loan?In the following exercises, translate to a system of equations and solve. 155. 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 $1095 in interest in one year?In the following exercises, translate to a system of equations and solve. 156. 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. 157. 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 $4,650 in interest on the two loans. How much is each loan?The manufacturer of an energy drink spends $1.20 to make each drink and sells them for $2. The manufacturer also has fixed costs each month of $8,000. (a) Find the cost function C when x energy drinks aremanufactured. (b) Find the revenue function R when x drinks are sold. (c) Show the break-even point by graphing both the Revenue and Cost functions on the same grid. (d) Find the break-even point. Interpret what the breakeven point means.The manufacturer of a water bottle spends $5 to build each bottle and sells them for $10. The manufacturer also has fixed costs each month of $6500. (a) Find the cost function C when x bottles are manufactured. (b) Find the revenue function R when x bottles are sold. (c) Show the break-even point by graphing both the Revenue and Cost functions on the same grid. (d) Find the break-even point. Interpret what the break-even point means.Take a handful of two types of coins, and write a problem similar to Example 4.25 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 4.28, we used elimination to solve the system of equations {s+b=40,0000.08s+0.03b=0.071( 40,000) . Could you have used substitution or elimination to solve this system? Why?Determine whether the ordered triple is a solution to the system: {3x+y+z=2x+2y+z=33z+y+2z=4 . (a) (1,3,2) (b) (4,1,5)Determine whether the ordered triple is a solution to the system: {x3y+z=53xyz=12x2y+3z=1 . (a) (2,2,3) (b) (2,2,3)Solve the system by elimination: {3x+yz=22x3y2z=14xy3z=0 .Solve the system by elimination: {4x+y+z=12x2y+z=22x+3yz=1 .Solve: {3x4z=12y+3z=22x+3y=6 .Solve: {4x3z=53y+2z=73x+4y=6 .Solve the system of equations: {x+2y+6z=5x+y2z=3x4y2z=1 .Solve the system of equations: {2x2y+3z=64x3y+2z=02x+3y7z=1 .Solve the system by equations: {x+yz=02x+4y2z=63x+6y3z=9 .Solve the system by equations: {xyz=1x+2y3z=43x2y7z=0 .The community college fine arts department sold three kinds of tickets to its latest dance presentation. The adult tickets sold for $20, the student tickets for $12 and the child tickets for $10.The fine arts department was thrilled to have sold 350 tickets and brought in $4,650 in one night. The number of child tickets sold is the same as the number of adult tickets sold. How many of each type did the department sell?The community college soccer team sold three kinds of tickets to its latest game. The adult tickets sold for $10, the student tickets for $8 and the child tickets for $5. The soccer team was thrilled to have sold 600 tickets and brought in $4,900 for one game. The number of adult tickets is twice the number of child tickets. How many of each type did the soccer team sell?In the following exercises, determine whether the ordered triple is a solution to the system. 162. {2x6y+z=33x4y3z=22x+3y2z=3 (a) (3,1,3) (b) (4,3,7)In the following exercises, determine whether the ordered triple is a solution to the system. 163. {3x+y+z=4x+2y2z=12xyz=1 (a) (5,7,4) (b) (5,7,4)In the following exercises, determine whether the ordered triple is a solution to the system. 164. {y10z=82xy=2x5z=3 (a) (7,12,2) (b) (2,2,1)In the following exercises, determine whether the ordered triple is a solution to the system. 165. {x+3yz=15y= 2 3x2x3y+z=2 (a) (6,5,12) (b) (5,43,3)In the following exercises, solve the system of equations. 166. {5x+2y+z=53xy+2z=62x+3y3z=5 In the following exercises, solve the system of equations. 167. {6x5y+2z=32x+y4z=33x3y+z=1 In the following exercises, solve the system of equations. 168. {2x5y+3z=83xy+4z=7x+3y+2z=3 In the following exercises, solve the system of equations. 169. {5x3y+2z=52xyz=43x2y+2z=7 In the following exercises, solve the system of equations. 170. {3x5y+4z=55x+2y+z=02x+3y2z=3 In the following exercises, solve the system of equations. 171. {4x3y+z=72x5y4z=33x2y2z=7 In the following exercises, solve the system of equations. 172. {3x+8y+2z=52x+5y3z=0x+2y2z=1 In the following exercises, solve the system of equations. 173. {11x+9y+2z=97x+5y+3z=74x+3y+z=3 In the following exercises, solve the system of equations. 174. { 1 3xyz=1x+ 5 2y+z=22x+2y+ 1 2z=4 In the following exercises, solve the system of equations. 175. {x+ 1 2y+ 1 2z=0 1 5x 1 5y+z=0 1 3x 1 3y+2z=1 In the following exercises, solve the system of equations. 176. {x+ 1 3y2z=1 1 3x+y+ 1 2z=0 1 2x+ 1 3y 1 2z=1 In the following exercises, solve the system of equations. 177. { 1 3xy+ 1 2z=4 2 3x+ 5 2y4z=0x 1 2y+ 3 2z=2 In the following exercises, solve the system of equations. 178. {x+2z=04y+3z=22x5y=3 In the following exercises, solve the system of equations. 179.{2x+5y=43yz=34x+3z=3 In the following exercises, solve the system of equations. 180. {2y+3z=15x+3y=67x+z=1 In the following exercises, solve the system of equations. 181. {3xz=35y+2z=64x+3y=8 In the following exercises, solve the system of equations. 182. {4x3y+2z=02x+3y7z=12x2y+3z=6 In the following exercises, solve the system of equations. 183. {x2y+2z=12x+yz=2xy+z=5 In the following exercises, solve the system of equations. 184. {2x+3y+z=12x+y+z=93x+4y+2z=20 In the following exercises, solve the system of equations. 185. {x+4y+z=84xy+3z=92x+7y+z=0 In the following exercises, solve the system of equations. 186. {x+2y+z=4x+y2z=32x3y+z=7 In the following exercises, solve the system of equations. 187. {x+y2z=32x3y+z=7x+2y+z=4 In the following exercises, solve the system of equations. 188. {x+y3z=1yz=0x+2y=1 In the following exercises, solve the system of equations. 189. {x2y+3z=1x+y3z=73x4y+5z=7 In the following exercises, solve the given problem. 190. The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is twice the measure if the first angle. The third angle is twelve more than the second. Find the measures of the three angles.In the following exercises, solve the given problem. 191. The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three the measure if the first angle. The third angle is fifteen more than the second. Find the measures of the three angles.In the following exercises, solve the given problem. 192. After watching a major musical production at the theater, the patrons can purchase souvenirs. If a family purchases 4 t-shirts, the video and 1 stuffed animal their total is $135. A couple buys 2 t-shirts, the video and 3 stuffed animal for their nieces and spends $115. Another couple buys 2 t-shirts, the video and 1 stuffed animal and their total is $85. What is the cost of each item?In the following exercises, solve the given problem. 193. The church youth group is selling snacks to raise money to attend their convention. Amy sold 2 pounds of candy, 3 boxes of cookies and 1 can of popcorn for a total sales of $65. Brian sold 4 pounds of candy, 6 boxes of cookies and 3 cans of popcorn for a total sales of $140. Paulina sold 8 pounds of candy, 8 boxes of cookies and 5 can of popcorn for a total sales of $250. What is the cost of each item?In your own words explain the steps to solve a system of linear equations with three variables by elimination.How can you tell when a system of three linear equations with three variables has no solution? Infinitely many solutions?Write each system of linear equations as an augmented matrix: (a) {3x+8y=32x=5y3 (b){2x5y+3z=83xy+4z=7x+3y+2z=3 Write each system of linear equations as an augmented matrix: (a) {11x=9y57x+5y=1 (b) {5x3y+2z=52xyz=43x2y+2z=7 Write the system of equations that corresponds to the augmented matrix: [112321214120] .Write the system of equations that corresponds to the augmented matrix: [111423181113] .Perform the indicated operations on the augmented matrix: (a) Interchange rows 1 and 3. (b) Multiply row 3 by 3. (c) Multiply row 3 by 2 and add to row 2. [522414230| 24 1]Perform the indicated operations on the augmented matrix: (a) Interchange rows 1 and 2, (b) Multiply row 1 by 2, (c) Multiply row 2 by 3 and add to row 1. [232413504| 42 1]Perform the needed row operation that will get the first entry in row 2 to be zero in the augmented matrix: [1136|22] .Perform the needed row operation that will get the first entry in row 2 to be zero in the augmented matrix: [1123|32] .Solve the system of equations using a matrix: {2x+y=7x2y=6 .Solve the system of equations using a matrix: {2x+y=4x2y=2 .Solve the system of equations using a matrix: {2x5y+3z=83xy+4z=7x+3y+2z=3 .Solve the system of equations using a matrix: {3x+y+z=4x+2y2z=12xyz=1 .Solve the system of equations using a matrix: {x2y+2z=12x+yz=2xy+z=5 .Solve the system of equations using a matrix: {3x+4y3z=22x+3yz=12x+y2z=6 .Solve the system of equations using a matrix: {x+yz=02x+4y2z=63x+6y3z=9 .Solve the system of equations using a matrix: {xyz=1x+2y3z=43x2y7z=0 .In the following exercises, write each system of linear equations as an augmented matrix. 196. (a) {3xy=12y=2x+5 (b) {4x+3y=2x2y3z=72xy+2z=6 In the following exercises, write each system of linear equations as an augmented matrix. 197. (a) {2x+4y=53x2y=2 (b) {3x2yz=22x+y=55x+4y+z=1 In the following exercises, write each system of linear equations as an augmented matrix. 198. (a) {3xy=42x=y+2 (b) {x3y4z=24x+2y+2z=52x5y+7z=8 In the following exercises, write each system of linear equations as an augmented matrix. 199. (a) {2x5y=34x=3y1 (b) {4x+3y2z=32x+y3z=4x4y+5z=2 Write the system of equations that that corresponds to the augmented matrix. 200. [2113|42]Write the system of equations that that corresponds to the augmented matrix. 201. [2433| 2 1]Write the system of equations that that corresponds to the augmented matrix. 202. [103120012| 1 23]Write the system of equations that that corresponds to the augmented matrix. 203. [220021301| 12 2]In the following exercises, perform the indicated operations on the augmented matrices. 204. [6432|31] (a) Interchange rows 1 and 2 (b) Multiply row 2 by 3 (c) Multiply row 2 by 2 and add to row 1.In the following exercises, perform the indicated operations on the augmented matrices. 205. [4632| 31] (a) Interchange rows 1 and 2 (b) Multiply row 1 by 4 (c) Multiply row 2 by 3 and add to row 1.In the following exercises, perform the indicated operations on the augmented matrices. 206. [132221423|4 3 1] (a) Interchange rows 2 and 3 (b) Multiply row 1 by 4 (c) Multiply row 2 by 2 and add to row 3.In the following exercises, perform the indicated operations on the augmented matrices. 207. [652214331|35 1] (a) Interchange rows 2 and 3 (b) Multiply row 2 by 5 (c) Multiply row 3 by 2 and add to row 1.In the following exercises, perform the indicated operations on the augmented matrices. 208. Perform the needed row operation that will get the first entry in row 2 to be zero in the augmented matrix:[1234|5 1] .In the following exercises, perform the indicated operations on the augmented matrices. 209. Perform the needed row operations that will get the first entry in both row 2 and row 3 to be zero in the augmented matrix: [123312234| 45 1] .In the following exercises, solve each system of equations using a matrix. 210. {2x+y=2xy=2 In the following exercises, solve each system of equations using a matrix. 211. {3x+y=2xy=2 In the following exercises, solve each system of equations using a matrix. 212. {x+2y=2x+y=4 In the following exercises, solve each system of equations using a matrix. 213. {2x+3y=3x+3y=12 In the following exercises, solve each system of equations using a matrix. 214. {2x3y+z=193x+y2z=15x+y+z=0 In the following exercises, solve each system of equations using a matrix. 215. {2xy+3z=3x+2yz=10x+y+z=5 In the following exercises, solve each system of equations using a matrix. 216. {2x6y+z=33x+2y3z=22x+3y2z=3 In the following exercises, solve each system of equations using a matrix. 217. {4x3y+z=72x5y4z=33x2y2z=7 In the following exercises, solve each system of equations using a matrix. 218. {x+2z=04y+3z=22x5y=3 In the following exercises, solve each system of equations using a matrix. 219. {2x+5y=43yz=34x+3z=3

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