# 5.5E: Exercises

- Page ID
- 30528

**More Practice: Money Problems**

- Two families bought tickets for the home basketball game. One family ordered \(2\) adult tickets and \(4\) children’s tickets for a total of \($36.00\). Another family ordered \(3\) adult tickets and \(2\) children’s tickets for a total of \($32.00\). How much did each ticket cost?
- Two friends found shirts and shorts on sale at a flea market. One bought \(4\) shirts and \(2\) shorts for a total of \($28.00\). The other bought \(3\) shirts and \(3\) shorts for a total of \($30.75\). How much was each shirt and each pair of shorts?
- A community theater sold \(140\) tickets to the evening musical for a total of \($1,540\). Each adult ticket was sold for \($12\) and each child ticket was sold for \($8\). How many adult tickets were sold?
- The campus bookstore sells graphing calculators for \($110\) and scientific calculators for \($16\). On the first day of classes \(50\) calculators were sold for a total of \($1,646\). How many of each were sold?
- Jim was able to purchase a pizza for \($12.35\) with quarters and dimes. If he uses \(71\) coins to buy the pizza, then how many of each did he have?
- A cash register contains \($5\) bills and \($10\) bills with a total value of \($350\). If there are \(46\) bills total, then how many of each does the register contain?
- A jar consisting of only nickels and quarters contains \(70\) coins. If the total value is \($9.10\), how many of each coin are in the jar?
- Jill has \($9.20\) worth of dimes and quarters. If there are \(68\) coins in total, how many of each does she have?

**Answer**-
1. Adults \($7.00\) each and children \($5.50\) each. 3. \(105\) adult tickets were sold.

5. \(35\) quarters and \(36\) dimes 7. The jar contains \(42\) nickels and \(28\) quarters

## More Practice: Combined fixed and variable costs

A taxi fare includes a fixed flat fee, plus a variable cost that depends on the number of miles driven.

Total manufacturing costs include a fixed overhead cost, plus a variable cost that depends on the number of items manufactured.

- In a moderate-size city, taxi fare is $51 for 12 miles and is $31 for 7 miles. What is the flat fee and what is the charge per mile?
- If it costs $90 to rent a car driven 100 miles and $140 for one driven 200 miles, find the daily rental fee and the mileage fee.
- To manufacture 30 items, it costs $2700, and to manufacture 50 items, it costs $3200. Find the overhead cost and the cost to manufacture one item
- To manufacture 100 items, it costs $32,000, and to manufacture 200 items, it costs $40,000. Find the overhead cost and the cost to manufacture one item
- If it costs a total of $750 to produce 20 items and the cost to manufacture an item is $25, what is the overhead cost?
- If it costs $1900 to manufacture 60 items, and the overhead is $700, what is the cost to produce one item?
- Sally earns \($1,000\) per month plus a commission of \(2\)% of sales. Jane earns \($200\) per month plus \(6\)% of her sales. At what monthly sales figure will both Sally and Jane earn the same amount of pay?
- The cost of producing specialty book shelves includes a daily production cost plus an additional cost per book shelf. The cost to produce 7 book shelves in 2 days was \($590\). The cost to produce 11 book shelves in 3 days was \( $910\). Find the daily cost and the cost for one bookshelf.

**Answers**-
1. \( \$ 4\) per mile 3. \( \$ 25\) per item; \( \$ 1950\) overhead costs. 5. \( \$ 250\) overhead 7. Sales of \($20,000\).

**More Practice: Percent Solution Problems**

Set up a linear system and solve.

1. A \(17\)% acid solution is to be mixed with a \(9\)% acid solution to produce \(8\) gallons of a \(10\)% acid solution. How much of each is needed?

2. A nurse wishes to obtain \(28\) ounces of a \(1.5\)% saline solution. How much of a \(1\)% saline solution must she mix with a \(4.5\)% saline solution to achieve the desired mixture?

3. A customer ordered \(4\) pounds of a mixed peanut product containing \(12\)% cashews. The inventory consists of only two mixes containing \(10\)% and \(26\)% cashews. How much of each type must be mixed to fill the order?

4. One alcohol solution contains \(10\)% alcohol and another contains \(25\)% alcohol. How much of each should be mixed together to obtain \(2\) gallons of a \(13.75\)% alcohol solution?

5. A \(50\)% fruit juice concentrate can be purchased wholesale. Best taste is achieved when water is mixed with the concentrate in such a way as to obtain a \(15\)% fruit juice mixture. How much water and concentrate is needed to make a \(60\)-ounce fruit juice drink?

6. How much cleaning fluid concentrate, with \(60\)% alcohol content, must be mixed with water to obtain a \(24\)-ounce mixture with \(15\)% alcohol content?

7. How many pounds of pure peanuts must be combined with a \(20\)% peanut mix to produce \(2\) pounds of a \(50\)% peanut mix?

8. Pure sugar is to be mixed with a fruit salad containing \(10\)% sugar to produce \(63\) ounces of a salad containing \(18\)% sugar. How much pure sugar is required?

9. A custom aluminum alloy is created by mixing \(150\) grams of a \(15\)% aluminum alloy and \(350\) grams of a \(55\)% aluminum alloy. What percentage of aluminum is in the resulting mixture?

10.A research assistant mixed \(500\) milliliters of a solution that contained a \(12\)% acid with \(300\) milliliters of water. What percentage of acid is in the resulting solution?

**Answer**-
1. \(7\) gallons of the \(9\)% acid solution and \(1\) gallon of the \(17\)% acid solution

3. \(3.5\) pounds of the \(10\)% cashew mix and \(0.5\) pounds of the \(26\)% cashew mix

5. \(18\) ounces of fruit juice concentrate and \(42\) ounces of water

7. \(.75\) pounds of pure peanuts

9. \(43\)%.

**More Practice: Per Cent Interest**

- A \($5,200\) principal is invested in two accounts, one earning \(3\)% interest and another earning \(6\)% interest. If the total interest for the year is \($210\), then how much is invested in each account?
- Harry’s \($2,200\) savings is in two accounts. One account earns \(2\)% annual interest and the other earns \(4\)%. His total interest for the year is \($69\). How much does he have in each account?
- Janine has two savings accounts totaling \($6,500\). One account earns \(2 \frac{3}{4}\)% annual interest and the other earns \(3 \frac{1}{2}\)%. If her total interest for the year is \($211\), then how much is in each account?
- Margaret has her total savings of \($24,200\) in two different CD accounts. One CD earns \(4.6\)% interest and another earns \(3.4\)% interest. If her total interest for the year is \($1,007.60\), then how much does she have in each CD account?
- Last year Mandy earned twice as much interest in her Money Market fund as she did in her regular savings account. The total interest from the two accounts was \($246\). How much interest did she earn in each account?
- A small business invested \($120,000\) in two accounts. The account earning \(4\)% annual interest yielded twice as much interest as the account earning \(3\)% annual interest. How much was invested in each account?

**Answer**-
1. \($3,400\) at \(3\)% and \($1,800\) at \(6\)%

3. \($2,200\) at \(2 \frac{3}{4}\)% and \($4,300\) at \(3 \frac{1}{2}\)%

5. Savings: \($82\); Money Market: \($164\).