Exercises: Solve Mixture and Uniform Motion Applications (3.8)
Exercises: Solve Coin Word Problems
Instructions: For questions 1-18, solve each coin word problem.
1. Jaime has [latex]$2.60[/latex] in dimes and nickels. The number of dimes is 14 more than the number of nickels. How many of each coin does he have?
Solution
[latex]8[/latex] nickels, [latex]22[/latex] dimes
2. Lee has [latex]$1.75[/latex] in dimes and nickels. The number of nickels is 11 more than the number of dimes. How many of each coin does he have?
3. Ngo has a collection of dimes and quarters with a total value of [latex]$3.50[/latex]. The number of dimes is seven more than the number of quarters. How many of each coin does he have?
Solution
[latex]15[/latex] dimes, [latex]8[/latex] quarters
4. Connor has a collection of dimes and quarters with a total value of [latex]$6.30[/latex]. The number of dimes is 14 more than the number of quarters. How many of each coin does he have?
5. A cash box of [latex]$1[/latex] and [latex]$5[/latex] bills is worth [latex]$45[/latex]. The number of [latex]$1[/latex] bills is three more than the number of [latex]$5[/latex]5 bills. How many of each bill does it contain?
Solution
[latex]10[/latex] at [latex]$1[/latex], [latex]7[/latex] at [latex]$5[/latex]
6. Joe’s wallet contains [latex]$1[/latex] and [latex]$5[/latex] bills worth [latex]$47[/latex]. The number of [latex]$1[/latex] bills is five more than the number of [latex]$5[/latex] bills. How many of each bill does he have?
7. Rachelle has [latex]$6.30[/latex] in nickels and quarters in her coin purse. The number of nickels is twice the number of quarters. How many coins of each type does she have?
Solution
[latex]18[/latex] quarters, [latex]36[/latex] nickels
8. Deloise has [latex]$1.20[/latex] in pennies and nickels in a jar on her desk. The number of pennies is three times the number of nickels. How many coins of each type does she have?
9. Harrison has [latex]$9.30[/latex] in his coin collection, all in pennies and dimes. The number of dimes is three times the number of pennies. How many coins of each type does he have?
Solution
[latex]30[/latex] pennies, [latex]90[/latex] dimes
10. Ivan has [latex]$8.75[/latex] in nickels and quarters in his desk drawer. The number of nickels is twice the number of quarters. How many coins of each type does he have?
11. In a cash drawer there is [latex]$125[/latex] in [latex]$5[/latex] and [latex]$10[/latex] bills. The number of [latex]$10[/latex] bills is twice the number of [latex]$5[/latex] bills. How many of each are in the drawer?
Solution
[latex]10[/latex] at [latex]$10[/latex], [latex]5[/latex] at [latex]$5[/latex]
12. John has [latex]$175[/latex] in [latex]$5[/latex] and [latex]$10[/latex] bills in his drawer. The number of [latex]$5[/latex] bills is three times the number of [latex]$10[/latex] bills. How many of each are in the drawer?
13. Carolyn has [latex]$2.55[/latex] in her purse in nickels and dimes. The number of nickels is nine less than three times the number of dimes. Find the number of each type of coin.
Solution
[latex]12[/latex] dimes and [latex]27[/latex] nickels
14. Julio has [latex]$2.75[/latex] in his pocket in nickels and dimes. The number of dimes is 10 less than twice the number of nickels. Find the number of each type of coin.
15. Chi has [latex]$11.30[/latex] in dimes and quarters. The number of dimes is three more than three times the number of quarters. How many of each are there?
Solution
[latex]63[/latex] dimes, [latex]20[/latex] quarters
16. Tyler has [latex]$9.70[/latex] in dimes and quarters. The number of quarters is eight more than four times the number of dimes. How many of each coin does he have?
17. Mukul has [latex]$3.75[/latex] in quarters, dimes and nickels in his pocket. He has five more dimes than quarters and nine more nickels than quarters. How many of each coin are in his pocket?
Solution
16 nickels, 12 dimes, 7 quarters
18. Vina has [latex]$4.70[/latex] in quarters, dimes and nickels in her purse. She has eight more dimes than quarters and six more nickels than quarters. How many of each coin are in her purse?
Exercises: Solve Ticket and Stamp Word Problems
Instructions: For questions 19-32, solve each ticket or stamp word problem.
19. The school play sold [latex]$550[/latex] in tickets one night. The number of [latex]$8[/latex] adult tickets was 10 less than twice the number of [latex]$5[/latex] child tickets. How many of each ticket were sold?
Solution
[latex]30[/latex] child tickets, [latex]50[/latex] adult tickets
20. If the number of [latex]$8[/latex] child tickets is seventeen less than three times the number of [latex]$12[/latex] adult tickets and the theater took in [latex]$584[/latex], how many of each ticket were sold?
21. The movie theater took in [latex]$1\text{,}220[/latex] one Monday night. The number of [latex]$7[/latex] child tickets was ten more than twice the number of [latex]$9[/latex] adult tickets. How many of each were sold?
Solution
[latex]110[/latex] child tickets, [latex]50[/latex] adult tickets
22. The ball game sold [latex]$1\text{,}340[/latex] in tickets one Saturday. The number of [latex]$12[/latex] adult tickets was 15 more than twice the number of [latex]$5[/latex] child tickets. How many of each were sold?
23. The ice rink sold [latex]95[/latex] tickets for the afternoon skating session, for a total of [latex]$828[/latex]. General admission tickets cost [latex]$10[/latex] each and youth tickets cost [latex]$8[/latex] each. How many general admission tickets and how many youth tickets were sold?
Solution
[latex]34[/latex] general, [latex]61[/latex] youth
24. For the 7:30 show time, [latex]140[/latex] movie tickets were sold. Receipts from the [latex]$13[/latex] adult tickets and the [latex]$10[/latex] senior tickets totaled [latex]1\text{,}664[/latex]. How many adult tickets and how many senior tickets were sold?
25. The box office sold [latex]360[/latex] tickets to a concert at the college. The total receipts were [latex]$4\text{,}170[/latex]. General admission tickets cost [latex]$15[/latex] and student tickets cost [latex]$10[/latex]. How many of each kind of ticket was sold?
Solution
[latex]114[/latex] general, [latex]246[/latex] student
26. Last Saturday, the museum box office sold [latex]281[/latex] tickets for a total of [latex]$3\text{,}954[/latex]. Adult tickets cost [latex]$15[/latex] and student tickets cost [latex]$12[/latex]. How many of each kind of ticket was sold?
27. Julie went to the post office and bought both [latex]$0.41[/latex] stamps and [latex]$0.26[/latex] postcards. She spent [latex]$51.40[/latex]. The number of stamps was 20 more than twice the number of postcards. How many of each did she buy?
Solution
[latex]40[/latex] postcards, [latex]100[/latex] stamps
28. Jason went to the post office and bought both [latex]$0.41[/latex] stamps and [latex]$0.26[/latex] postcards and spent [latex]$10.28[/latex]. The number of stamps was four more than twice the number of postcards. How many of each did he buy?
29. Maria spent [latex]$12.50[/latex] at the post office. She bought three times as many [latex]$0.41[/latex] stamps as [latex]$0.02[/latex] stamps. How many of each did she buy?
Solution
[latex]30[/latex] at [latex]$0.41[/latex], [latex]10[/latex] at [latex]$0.02[/latex]
30. Hector spent [latex]$33.20[/latex] at the post office. He bought four times as many [latex]$0.41[/latex] stamps as [latex]$0.02[/latex] stamps. How many of each did he buy?
31. Hilda has [latex]$210[/latex] worth of [latex]$10[/latex] and [latex]$12[/latex] stock shares. The numbers of [latex]$10[/latex] shares is five more than twice the number of [latex]$12[/latex] shares. How many of each does she have?
Solution
[latex]15[/latex] [latex]$10[/latex] shares, [latex]5[/latex] [latex]$12[/latex] shares
32. Mario invested [latex]$475[/latex] in [latex]$45[/latex] and [latex]$25[/latex] stock shares. The number of [latex]$25[/latex] shares was five less than three times the number of [latex]$45[/latex] shares. How many of each type of share did he buy?
Exercises: Solve Mixture Word Problems
Instructions: For questions 33-44, solve each mixture word problem.
33. Lauren in making [latex]15[/latex] liters of mimosas for a brunch banquet. Orange juice costs her [latex]$1.50[/latex] per liter and champagne costs her [latex]$12[/latex] per liter. How many liters of orange juice and how many liters of champagne should she use for the mimosas to cost Lauren [latex]$5[/latex] per liter?
Solution
[latex]5[/latex] liters champagne, [latex]10[/latex] liters orange juice
34. Macario is making [latex]12[/latex] pounds of nut mixture with macadamia nuts and almonds. Macadamia nuts cost [latex]$9[/latex] per pound and almonds cost [latex]$5.25[/latex] per pound. How many pounds of macadamia nuts and how many pounds of almonds should Macario use for the mixture to cost [latex]$6.50[/latex] per pound to make?
35. Kaapo is mixing Kona beans and Maui beans to make [latex]25[/latex] pounds of coffee blend. Kona beans cost Kaapo [latex]$15[/latex] per pound and Maui beans cost [latex]$24[/latex] per pound. How many pounds of each coffee bean should Kaapo use for his blend to cost him [latex]$17.70[/latex] per pound?
Solution
[latex]7.5[/latex] lbs Maui beans, [latex]17.5[/latex] Kona beans
36. Estelle is making [latex]30[/latex] pounds of fruit salad from strawberries and blueberries. Strawberries cost [latex]$1.80[/latex] per pound and blueberries cost [latex]$4.50[/latex] per pound. If Estelle wants the fruit salad to cost her [latex]$2.52[/latex] per pound, how many pounds of each berry should she use?
37. Carmen wants to tile the floor of his house. He will need [latex]1000[/latex] square feet of tile. He will do most of the floor with a tile that costs [latex]$1.50[/latex] per square foot, but also wants to use an accent tile that costs [latex]$9.00[/latex] per square foot. How many square feet of each tile should he plan to use if he wants the overall cost to be [latex]$3[/latex] per square foot?
Solution
[latex]800[/latex] at [latex]$1.50[/latex], [latex]200[/latex] at [latex]$9.00[/latex]
38. Riley is planning to plant a lawn in his yard. He will need nine pounds of grass seed. He wants to mix Bermuda seed that costs [latex]$4.80[/latex] per pound with Fescue seed that costs [latex]$3.50[/latex] per pound. How much of each seed should he buy so that the overall cost will be [latex]$4.02[/latex] per pound?
39. Vartan was paid [latex]$25\text{,}000[/latex] for a cell phone app that he wrote and wants to invest it to save for his son’s education. He wants to put some of the money into a bond that pays [latex]4\%[/latex] annual interest and the rest into stocks that pay [latex]9\%[/latex] annual interest. If he wants to earn [latex]7.4\%[/latex] annual interest on the total amount, how much money should he invest in each account?
Solution
[latex]$8\text{,}000[/latex] at [latex]4\%[/latex], [latex]$17\text{,}000[/latex] at [latex]9\%[/latex]
40. Vern sold his 1964 Ford Mustang for [latex]$55\text{,}000[/latex] and wants to invest the money to earn him [latex]5.8\%[/latex] interest per year. He will put some of the money into Fund A that earns [latex]3\%[/latex] per year and the rest in Fund B that earns [latex]10\%[/latex] per year. How much should he invest into each fund if he wants to earn [latex]5.8\%[/latex] interest per year on the total amount?
41. Stephanie inherited [latex]$40\text{,}000[/latex]. She wants to put some of the money in a certificate of deposit that pays [latex]2.1\%[/latex] interest per year and the rest in a mutual fund account that pays [latex]6.5\%[/latex] per year. How much should she invest in each account if she wants to earn [latex]5.4\%[/latex] interest per year on the total amount?
Solution
[latex]$10\text{,}000[/latex] in CD, [latex]$30\text{,}000[/latex] in mutual fund
42. Avery and Caden have saved [latex]$27\text{,}000[/latex] towards a down payment on a house. They want to keep some of the money in a bank account that pays [latex]2.4\%[/latex] annual interest and the rest in a stock fund that pays [latex]7.2\%[/latex] annual interest. How much should they put into each account so that they earn [latex]6\%[/latex] interest per year?
43. Dominic pays [latex]7\%[/latex] interest on his [latex]$15\text{,}000[/latex] college loan and [latex]12\%[/latex] interest on his [latex]$11\text{,}000[/latex] car loan. What average interest rate does he pay on the total [latex]$26\text{,}000[/latex] he owes? (Round your answer to the nearest tenth of a percent.)
Solution
[latex]9.1\%[/latex]
44. Liam borrowed a total of [latex]$35\text{,}000[/latex] to pay for college. He pays his parents [latex]3\%[/latex] interest on the [latex]$8\text{,}000[/latex] he borrowed from them and pays the bank [latex]6.8\%[/latex] on the rest. What average interest rate does he pay on the total [latex]$35\text{,}000[/latex]? (Round your answer to the nearest tenth of a percent.)
Exercises: Solve Uniform Motion Applications
Instructions: For questions 45-66, solve.
45. Lilah is moving from Portland to Seattle. It takes her three hours to go by train. Mason leaves the train station in Portland and drives to the train station in Seattle with all Lilah’s boxes in his car. It takes him [latex]2.4[/latex] hours to get to Seattle, driving at [latex]15[/latex] miles per hour faster than the speed of the train. Find Mason’s speed and the speed of the train.
Solution
Mason [latex]75[/latex] mph, train [latex]60[/latex] mph
46. Kathy and Cheryl are walking in a fundraiser. Kathy completes the course in [latex]4.8 hours[/latex] and Cheryl completes the course in [latex]8[/latex] hours. Kathy walks two miles per hour faster than Cheryl. Find Kathy’s speed and Cheryl’s speed.
47. Two buses go from Sacramento for San Diego. The express bus makes the trip in [latex]6.8[/latex] hours and the local bus takes [latex]10.2[/latex] hours for the trip. The speed of the express bus is [latex]25[/latex] mph faster than the speed of the local bus. Find the speed of both buses.
Solution
express bus [latex]75[/latex] mph, local [latex]50[/latex] mph
48. A commercial jet and a private airplane fly from Denver to Phoenix. It takes the commercial jet [latex]1.1[/latex] hours for the flight, and it takes the private airplane [latex]1.8[/latex] hours. The speed of the commercial jet is [latex]210[/latex] miles per hour faster than the speed of the private airplane. Find the speed of both airplanes.
49. Saul drove his truck [latex]3[/latex] hours from Dallas towards Kansas City and stopped at a truck stop to get dinner. At the truck stop he met Erwin, who had driven [latex]4[/latex] hours from Kansas City towards Dallas. The distance between Dallas and Kansas City is [latex]542[/latex] miles, and Erwin’s speed was eight miles per hour slower than Saul’s speed. Find the speed of the two truckers.
Solution
Saul [latex]82[/latex] mph, Erwin [latex]74[/latex] mph
50. Charlie and Violet met for lunch at a restaurant between Memphis and New Orleans. Charlie had left Memphis and drove [latex]4.8[/latex] hours towards New Orleans. Violet had left New Orleans and drove [latex]2[/latex] hours towards Memphis, at a speed 10 miles per hour faster than Charlie’s speed. The distance between Memphis and New Orleans is [latex]394[/latex] miles. Find the speed of the two drivers.
51. Sisters Helen and Anne live [latex]332[/latex] miles apart. For Thanksgiving, they met at their other sister’s house partway between their homes. Helen drove [latex]3.2[/latex] hours and Anne drove [latex]2.8[/latex] hours. Helen’s average speed was four miles per hour faster than Anne’s. Find Helen’s average speed and Anne’s average speed.
Solution
Helen [latex]60[/latex] mph, Anne [latex]56[/latex] mph
52. Ethan and Leo start riding their bikes at the opposite ends of a [latex]65[/latex]-mile bike path. After Ethan has ridden [latex]1.5[/latex] hours and Leo has ridden [latex]2[/latex] hours, they meet on the path. Ethan’s speed is six miles per hour faster than Leo’s speed. Find the speed of the two bikers.
53. Elvira and Aletheia live [latex]3.1[/latex] miles apart on the same street. They are in a study group that meets at a coffee shop between their houses. It took Elvira half an hour and Aletheia two-thirds of an hour to walk to the coffee shop. Aletheia’s speed is [latex]0.6[/latex] miles per hour slower than Elvira’s speed. Find both women’s walking speeds.
Solution
Aletheia [latex]2.4[/latex] mph, Elvira [latex]3[/latex] mph
54. DaMarcus and Fabian live [latex]23[/latex] miles apart and play soccer at a park between their homes. DaMarcus rode his bike for three-quarters of an hour and Fabian rode his bike for half an hour to get to the park. Fabian’s speed was six miles per hour faster than DaMarcus’ speed. Find the speed of both soccer players.
55. Cindy and Richard leave their dorm in Charleston at the same time. Cindy rides her bicycle north at a speed of [latex]18[/latex] miles per hour. Richard rides his bicycle south at a speed of [latex]14[/latex] miles per hour. How long will it take them to be [latex]96[/latex] miles apart?
Solution
[latex]3[/latex] hours
56. Matt and Chris leave their uncle’s house in Phoenix at the same time. Matt drives west on I-60 at a speed of [latex]76[/latex] miles per hour. Chris drives east on I-60 at a speed of [latex]82[/latex] miles per hour. How many hours will it take them to be [latex]632[/latex] miles apart?
57. Two buses leave Billings at the same time. The Seattle bus heads west on I-90 at a speed of [latex]73[/latex] miles per hour while the Chicago bus heads east at a speed of [latex]79[/latex] miles an hour. How many hours will it take them to be [latex]532[/latex] miles apart?
Solution
[latex]3.5[/latex] hours
58. Two boats leave the same dock in Cairo at the same time. One heads north on the Mississippi River while the other heads south. The northbound boat travels four miles per hour. The southbound boat goes eight miles per hour. How long will it take them to be [latex]54[/latex] miles apart?
59. Lorena walks the path around the park in [latex]30[/latex] minutes. If she jogs, it takes her [latex]20[/latex] minutes. Her jogging speed is [latex]1.5[/latex] miles per hour faster than her walking speed. Find Lorena’s walking speed and jogging speed.
Solution
walking [latex]3[/latex] mph, jogging [latex]4.5[/latex] mph
60. Julian rides his bike uphill for [latex]45[/latex] minutes, then turns around and rides back downhill. It takes him [latex]15[/latex] minutes to get back to where he started. His uphill speed is [latex]3.2[/latex] miles per hour slower than his downhill speed. Find Julian’s uphill and downhill speed.
61. Cassius drives his boat upstream for [latex]45[/latex] minutes. It takes him [latex]30[/latex] minutes to return downstream. His speed going upstream is three miles per hour slower than his speed going downstream. Find his upstream and downstream speeds.
Solution
upstream [latex]6[/latex] mph, downstream [latex]9[/latex] mph
62. It takes Darline [latex]20[/latex] minutes to drive to work in light traffic. To come home, when there is heavy traffic, it takes her [latex]36[/latex] minutes. Her speed in light traffic is [latex]24[/latex] miles per hour faster than her speed in heavy traffic. Find her speed in light traffic and in heavy traffic.
63. At 1:30, Marlon left his house to go to the beach, a distance of [latex]7.6[/latex] miles. He rode his skateboard until 2:15, then walked the rest of the way. He arrived at the beach at 3:00. Marlon’s speed on his skateboard is 2.5 times his walking speed. Find his speed when skateboarding and when walking.
Solution
skateboarding [latex]8[/latex] mph, walking [latex]3.2[/latex] mph
64. Aaron left at 9:15 to drive to his mountain cabin [latex]108[/latex] miles away. He drove on the freeway until 10:45, and then he drove on the mountain road. He arrived at 11:05. His speed on the freeway was three times his speed on the mountain road. Find Aaron’s speed on the freeway and on the mountain road.
65. Marisol left Los Angeles at 2:30 to drive to Santa Barbara, a distance of [latex]95[/latex] miles. The traffic was heavy until 3:20. She drove the rest of the way in very light traffic and arrived at 4:20. Her speed in heavy traffic was [latex]40[/latex] miles per hour slower than her speed in light traffic. Find her speed in heavy traffic and in light traffic.
Solution
heavy traffic [latex]30[/latex] mph, light traffic [latex]70[/latex] mph
66. Lizette is training for a marathon. At 7:00, she left her house and ran until 8:15, then she walked until 11:15. She covered a total distance of [latex]19[/latex] miles. Her running speed was five miles per hour faster than her walking speed. Find her running and walking speeds.
Exercises: Everyday Math
Instructions: For questions 67-70, answer the given everyday math word problems.
67. As the treasurer of her daughter’s Girl Scout troop, Laney collected money for some girls and adults to go to a 3-day camp. Each girl paid [latex]$75[/latex] and each adult paid [latex]$30[/latex]. The total amount of money collected for camp was [latex]$765[/latex]. If the number of girls is three times the number of adults, how many girls and how many adults paid for camp?
Solution
[latex]9[/latex] girls, [latex]3[/latex] adults
68. 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 [latex]$15[/latex] full-year registration fee and how many had paid the [latex]$10[/latex] 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 [latex]$250[/latex] was collected for all the registrations, how many boys had paid the full-year fee and how many had paid the partial-year fee?
69. John left his house in Irvine at 8:35 am to drive to a meeting in Los Angeles, [latex]45[/latex] miles away. He arrived at the meeting at 9:50. At 3:30 pm, he left the meeting and drove home. He arrived home at 5:18.
a. What was his average speed on the drive from Irvine to Los Angeles?
b. What was his average speed on the drive from Los Angeles to Irvine?
c. What was the total time he spent driving to and from this meeting?
d. John drove a total of [latex]90[/latex] miles roundtrip. Find his average speed. (Round to the nearest tenth.)
Solution
a. [latex]36[/latex] mph
b. [latex]25[/latex] mph
c. [latex]3.05[/latex] hours
d. [latex]29.5[/latex] mph
70. Sarah wants to arrive at her friend’s wedding at 3:00. The distance from Sarah’s house to the wedding is [latex]95[/latex] miles. Based on usual traffic patterns, Sarah predicts she can drive the first [latex]15[/latex] miles at [latex]60[/latex] miles per hour, the next [latex]10[/latex] miles at [latex]30[/latex] miles per hour, and the remainder of the drive at [latex]70[/latex] miles per hour.
a. How long will it take Sarah to drive the first [latex]15[/latex] miles?
b. How long will it take Sarah to drive the next [latex]10[/latex] miles?
c. How long will it take Sarah to drive the rest of the trip?
d. What time should Sarah leave her house?
Exercises: Writing Exercises
Instructions: For questions 71-76, answer the given writing exercises.
71. Suppose you have six quarters, nine dimes, and four pennies. Explain how you find the total value of all the coins.
Solution
Answers will vary.
72. Do you find it helpful to use a table when solving coin problems? Why or why not?
73. In the table used to solve coin problems, one column is labeled “number” and another column is labeled “value.” What is the difference between the “number” and the “value?”
Solution
Answers will vary.
74. What similarities and differences did you see between solving the coin problems and the ticket and stamp problems?
75. When solving a uniform motion problem, how does drawing a diagram of the situation help you?
Solution
Answers will vary.
76. When solving a uniform motion problem, how does creating a table help you?
