Let’s solve each problem step by step using proportions. The key idea is:
Part / Whole = Percent / 100
We’ll go through each lettered problem one at a time.
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a. What number is 30% of 150?
Set up proportion:
x / 150 = 30 / 100
Cross multiply:
100x = 30 × 150 → 100x = 4500
Divide both sides by 100:
x = 45
✔ Answer:
45
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b. 30 is what percent of 150?
Set up proportion:
30 / 150 = x / 100
Simplify left side: 30 ÷ 150 = 1/5 → so 1/5 = x/100
Cross multiply:
5x = 100 → x = 20
✔ Answer:
20%
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c. 90 is 60% of what number?
Set up proportion:
90 / x = 60 / 100
Cross multiply:
60x = 90 × 100 → 60x = 9000
Divide by 60:
x = 150
✔ Answer:
150
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d. 25 is what % of 500?
Set up proportion:
25 / 500 = x / 100
Simplify left: 25 ÷ 500 = 1/20 → 1/20 = x/100
Cross multiply:
20x = 100 → x = 5
✔ Answer:
5%
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e. 40 is 500% of what number?
Set up proportion:
40 / x = 500 / 100
Simplify right: 500/100 = 5 → so 40/x = 5
Then: 5x = 40 → x = 8
✔ Answer:
8
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f. Find 12% of 75.
Set up proportion:
x / 75 = 12 / 100
Cross multiply:
100x = 12 × 75 → 100x = 900
x = 9
✔ Answer:
9
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g. 16 is ___% of 160?
Set up proportion:
16 / 160 = x / 100
Simplify left: 16 ÷ 160 = 1/10 → 1/10 = x/100
Cross multiply:
10x = 100 → x = 10
✔ Answer:
10%
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h. 160 is 16% of ___?
Set up proportion:
160 / x = 16 / 100
Cross multiply:
16x = 160 × 100 → 16x = 16000
x = 1000
✔ Answer:
1000
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i. ___ is 125% of 8?
Set up proportion:
x / 8 = 125 / 100
Cross multiply:
100x = 125 × 8 → 100x = 1000
x = 10
✔ Answer:
10
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j. 975 is 75% of what number?
Set up proportion:
975 / x = 75 / 100
Cross multiply:
75x = 975 × 100 → 75x = 97500
Divide by 75:
x = 1300
✔ Answer:
1300
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Final Answer:
a. 45
b. 20%
c. 150
d. 5%
e. 8
f. 9
g. 10%
h. 1000
i. 10
j. 1300
Parent Tip: Review the logic above to help your child master the concept of percent proportion worksheet answers.
