Question

6.2 extra practice
write and solve a proportion to answer the questions
a. what number is 25% of 60?
b. 30 is what percent of 80?
c. 20 is 40% of what number?
d. what number is 110% of 70?
e. 32 is what percent of 128?
f. what percent of 48 is 36?
g. 12 is what percent of 60?
h. 8% of what number is 16?
i. 42 is 8% of what number?
j. 30% of 140 is what number?
k. 150% of 22 is what number?
l. what number is 0.6% of 30?
m. the seventh-grade class needs to earn money for a
trip to the amusement park. of the 160 seventh-grade
students, 60% participate in the fundraiser. how many
students participate in the fundraiser?

Explanation:

Step1: Define percent proportion formula

The core proportion for all problems is $\frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100}$, where we solve for the unknown value.

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Part A: What number is 25% of 60?

Step1: Set up proportion

Let $x$ = unknown number. $\frac{x}{60} = \frac{25}{100}$

Step2: Solve for $x$

$x = 60 \times \frac{25}{100}$
$x = 60 \times 0.25 = 15$

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Part B: 30 is what percent of 80?

Step1: Set up proportion

Let $p$ = unknown percent. $\frac{30}{80} = \frac{p}{100}$

Step2: Solve for $p$

$p = \frac{30}{80} \times 100$
$p = 0.375 \times 100 = 37.5$

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Part C: 20 is 40% of what number?

Step1: Set up proportion

Let $x$ = unknown number. $\frac{20}{x} = \frac{40}{100}$

Step2: Solve for $x$

$x = 20 \times \frac{100}{40}$
$x = 20 \times 2.5 = 50$

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Part D: What number is 110% of 70?

Step1: Set up proportion

Let $x$ = unknown number. $\frac{x}{70} = \frac{110}{100}$

Step2: Solve for $x$

$x = 70 \times \frac{110}{100}$
$x = 70 \times 1.1 = 77$

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Part E: 32 is what percent of 128?

Step1: Set up proportion

Let $p$ = unknown percent. $\frac{32}{128} = \frac{p}{100}$

Step2: Solve for $p$

$p = \frac{32}{128} \times 100$
$p = 0.25 \times 100 = 25$

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Part F: What percent of 48 is 36?

Step1: Set up proportion

Let $p$ = unknown percent. $\frac{36}{48} = \frac{p}{100}$

Step2: Solve for $p$

$p = \frac{36}{48} \times 100$
$p = 0.75 \times 100 = 75$

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Part G: 12 is what percent of 60?

Step1: Set up proportion

Let $p$ = unknown percent. $\frac{12}{60} = \frac{p}{100}$

Step2: Solve for $p$

$p = \frac{12}{60} \times 100$
$p = 0.2 \times 100 = 20$

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Part H: 8% of what number is 16?

Step1: Set up proportion

Let $x$ = unknown number. $\frac{16}{x} = \frac{8}{100}$

Step2: Solve for $x$

$x = 16 \times \frac{100}{8}$
$x = 16 \times 12.5 = 200$

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Part I: 42 is 8% of what number?

Step1: Set up proportion

Let $x$ = unknown number. $\frac{42}{x} = \frac{8}{100}$

Step2: Solve for $x$

$x = 42 \times \frac{100}{8}$
$x = 42 \times 12.5 = 525$

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Part J: 30% of 140 is what number?

Step1: Set up proportion

Let $x$ = unknown number. $\frac{x}{140} = \frac{30}{100}$

Step2: Solve for $x$

$x = 140 \times \frac{30}{100}$
$x = 140 \times 0.3 = 42$

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Part K: 150% of 22 is what number?

Step1: Set up proportion

Let $x$ = unknown number. $\frac{x}{22} = \frac{150}{100}$

Step2: Solve for $x$

$x = 22 \times \frac{150}{100}$
$x = 22 \times 1.5 = 33$

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Part L: What number is 0.6% of 30?

Step1: Set up proportion

Let $x$ = unknown number. $\frac{x}{30} = \frac{0.6}{100}$

Step2: Solve for $x$

$x = 30 \times \frac{0.6}{100}$
$x = 30 \times 0.006 = 0.18$

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Part M: How many students participate?

Step1: Set up proportion

Let $x$ = number of students. $\frac{x}{160} = \frac{60}{100}$

Step2: Solve for $x$

$x = 160 \times \frac{60}{100}$
$x = 160 \times 0.6 = 96$

Answer:

A. 15
B. 37.5%
C. 50
D. 77
E. 25%
F. 75%
G. 20%
H. 200
I. 525
J. 42
K. 33
L. 0.18
M. 96