Question

name
date
solving proportions
n - gen math® 7 homework
fluency

1. solve each of the following proportions for the variables given without the use of a calculator.

(a) \\(\frac{c}{8}=6\\)
(b) \\(\frac{x}{14}=\frac{3}{7}\\)
(c) \\(\frac{36}{m}=\frac{12}{5}\\)

1. solve each of the following proportions using a calculator to aid in calculations.

(a) \\(\frac{a}{39}=\frac{1.4}{6}\\)
(b) \\(\frac{377}{x}=\frac{13}{5}\\)
(c) \\(\frac{10}{3}=\frac{115}{c}\\)
using your math (use a calculator to help)

1. rachel is getting a sundae where the cost is proportional to the weight of the sundae she makes. last time rachel went she bought a 12 - ounce sundae for $4.20. this time she buys a 17 - ounce sundae. let c be the cost of the sundae. set up and solve a proportion for c.

n - gen math® 7, unit 3 - proportional relationships - lesson 4
©mathinstruction, red hook, ny 12571, © 2029

Explanation:

Step1: Cross-multiply to isolate $c$

$\frac{c}{8}=6 \implies c=6 \times 8$

Step2: Calculate the value of $c$

$c=48$

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Step1: Cross-multiply to isolate $x$

$\frac{x}{14}=\frac{3}{7} \implies 7x=14 \times 3$

Step2: Simplify right-hand side

$7x=42$

Step3: Solve for $x$

$x=\frac{42}{7}=6$

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Step1: Cross-multiply to isolate $m$

$\frac{36}{m}=\frac{12}{5} \implies 12m=36 \times 5$

Step2: Simplify right-hand side

$12m=180$

Step3: Solve for $m$

$m=\frac{180}{12}=15$

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Step1: Cross-multiply to isolate $a$

$\frac{a}{39}=\frac{14}{6} \implies 6a=39 \times 14$

Step2: Simplify right-hand side

$6a=546$

Step3: Solve for $a$

$a=\frac{546}{6}=91$

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Step1: Cross-multiply to isolate $x$

$\frac{377}{x}=\frac{13}{5} \implies 13x=377 \times 5$

Step2: Simplify right-hand side

$13x=1885$

Step3: Solve for $x$

$x=\frac{1885}{13}=145$

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Step1: Cross-multiply to isolate $c$

$\frac{10}{3}=\frac{115}{c} \implies 10c=3 \times 115$

Step2: Simplify right-hand side

$10c=345$

Step3: Solve for $c$

$c=\frac{345}{10}=34.5$

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Step1: Set up proportional equation

$\frac{\text{Cost}}{\text{Weight}} = \frac{4.20}{12}=\frac{c}{17}$

Step2: Cross-multiply to isolate $c$

$12c=4.20 \times 17$

Step3: Simplify right-hand side

$12c=71.4$

Step4: Solve for $c$

$c=\frac{71.4}{12}=5.95$

Answer:

1. (a) $c=48$

(b) $x=6$
(c) $m=15$

1. (a) $a=91$

(b) $x=145$
(c) $c=34.5$

1. $c=\$5.95$