Question

complete the problems. check your answers in the back of the book.

1. copy center charges 8¢ a page for machine - fed copies and 20¢ per page for hand - fed copies. if logan kaminski’s bill for 80 copies of his movie script is $13.00, how many copies of each type were made?
2. mary tuttle owns a carpet - cleaning business. she charges $67.95 for a two - bedroom house and $82.25 for a three - bedroom house. last month the company had gross receipts of $4,413.00 for cleaning carpet in 8 more three - bedroom houses than two - bedroom houses. how many of each type did the company clean?

lesson practice
complete the table.

worker	rate per item	×	number of items	=	total pay
6. dressler, ginger	0.06	×	4,234	=
7. danielli, ella	0.19	×	719	=
8. koop, evan	15.625	×	326	=
9. dawson, ted	658.55	×	a	=	$71,781.95
10. orlov, irina	a	×	15	=	$32,179.95

1. anthony harris earns $0.50 per hamper of heirloom tomatoes. one day he picked 43 hampers - worth. what was his total pay that day?
2. your aunt and uncle ask you to hang pictures in their home. they offer to pay you $3.50 per picture. what is your total pay if you hang 15 pictures?
3. lee wu writes 48 résumés for $35 each. what is her pay?
4. craig rose is an over - the - road truck driver. if he is paid $0.54 per mile, what is craig’s total pay for the day he drove 527 miles?

Explanation:

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Problem 3

Step1: Define variables

Let $x$ = number of machine-fed copies, $y$ = number of hand-fed copies.

Step2: Set up total copies equation

$x + y = 80$

Step3: Set up total cost equation

Convert cents to dollars: $0.08x + 0.20y = 13.00$

Step4: Solve for $x$ from Step2

$x = 80 - y$

Step5: Substitute into cost equation

$0.08(80 - y) + 0.20y = 13.00$
$6.4 - 0.08y + 0.20y = 13.00$
$0.12y = 6.6$

Step6: Solve for $y$

$y = \frac{6.6}{0.12} = 55$

Step7: Solve for $x$

$x = 80 - 55 = 25$

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Problem 4

Step1: Define variables

Let $a$ = number of two-bedroom houses, $b$ = number of three-bedroom houses.

Step2: Set up quantity relation

$b = a + 8$

Step3: Set up gross receipts equation

$67.95a + 82.25b = 4413.00$

Step4: Substitute $b$ into receipts equation

$67.95a + 82.25(a + 8) = 4413.00$
$67.95a + 82.25a + 658 = 4413.00$
$150.2a = 3755$

Step5: Solve for $a$

$a = \frac{3755}{150.2} = 25$

Step6: Solve for $b$

$b = 25 + 8 = 33$

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Problems 5-10 (Table Completion)

Step1: Problem5: Calculate total pay

$\text{Total Pay} = 1.45 \times 340 = 493$

Step2: Problem6: Calculate total pay

$\text{Total Pay} = 0.06 \times 4234 = 254.04$

Step3: Problem7: Calculate total pay

$\text{Total Pay} = 0.19 \times 719 = 136.61$

Step4: Problem8: Calculate total pay

$\text{Total Pay} = 15.625 \times 326 = 5093.75$

Step5: Problem9: Solve for $a$

$a = \frac{71781.95}{658.55} = 109$

Step6: Problem10: Solve for $a$

$a = \frac{32179.95}{15} = 2145.33$

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Problem 11

Step1: Calculate total pay

$\text{Total Pay} = 0.50 \times 43 = 21.50$

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Problem 12

Step1: Calculate total pay

$\text{Total Pay} = 3.50 \times 15 = 52.50$

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Problem 13

Step1: Calculate total pay

$\text{Total Pay} = 35 \times 48 = 1680$

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Problem 14

Step1: Calculate total pay

$\text{Total Pay} = 0.54 \times 527 = 284.58$

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Answer:

1. 25 machine-fed copies, 55 hand-fed copies
2. 25 two-bedroom houses, 33 three-bedroom houses
3. $\$493$
4. $\$254.04$
5. $\$136.61$
6. $\$5093.75$
7. $a=109$
8. $a=\$2145.33$
9. $\$21.50$
10. $\$52.50$
11. $\$1680$
12. $\$284.58$