4.3 Solve Mixture Applications with Systems of Equations

Two-variable models for blending solutions, splitting an investment across interest rates, and finding the break-even point of cost and revenue functions.

Intermediate Algebra 2e, 4.3 Solve Mixture Applications with Systems of Equations

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32 exercises

4.3 Exercise 1

Before you get started, take this readiness quiz.

Multiply: $4.025 \left(1,562\right) .$
If you missed this problem, review the reference.

2.5

4.3 Exercise 2

Write 8.2% as a decimal.
If you missed this problem, review the reference.

2.5

4.3 Exercise 3

Earl’s dinner bill came to $32.50 and he wanted to leave an 18% tip. How much should the tip be?
If you missed this problem, review the reference.

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4.3 Exercise 5

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?

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4.3 Exercise 6

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?

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4.3 Exercise 8

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?

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4.3 Exercise 9

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?

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4.3 Exercise 11

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?

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4.3 Exercise 12

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 g…

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4.3 Exercise 14

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?

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4.3 Exercise 15

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?

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4.3 Exercise 17

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?

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4.3 Exercise 18

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?

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4.3 Exercise 20

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?

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4.3 Exercise 21

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?

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