Percent of a Number Examples: 46 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Percent of a Number.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Calculating a given percentage of a quantity by converting the percent to a decimal (or fraction) and multiplying.

$25\%$ of 80 means 'one quarter of 80.' Convert $25\%$ to $0.25$ and multiply: $0.25 \times 80 = 20$ .

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A percent of a number converts the percent to a decimal or fraction and multiplies the whole by it.

Common stuck point: The procedure for percent of a number is the easy part; the trap is multiplying by the percent without dividing by 100 first. Asking "Am I taking a stated percent of a given quantity?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I taking a stated percent of a given quantity?

Worked Examples

Example 1

easy

Find

35\%

140

35% of 140 — the shaded 7 out of 20 parts shows 35%; find the value

Answer

49

First step

Convert the percentage to a decimal:

35\% = 0.35

Full solution

2
Multiply: $0.35 \times 140 = 49$ .
3
Alternatively: $\frac{35}{100} \times 140 = \frac{35 \times 140}{100} = \frac{4900}{100} = 49$ .

Percent of a number follows the pattern: Part = (Percent ÷ 100) × Whole. Converting the percent to a decimal first is the most direct calculation method.

Example 2

medium

A store offers a

40\%

discount on a jacket priced at

\$85

. What is the sale price?

Example 3

easy

What is

75\%

80

75% of 80 — three quarters of the circle are shaded; find their value

Example 4

medium

A restaurant bill is $72. You leave an

18\%

tip. How much is the tip?

Example 5

medium

A jacket is marked down

30\%

from $80. What is the sale price?

30% off $80 — 3 sections = discount ($24); 7 shaded sections = sale price (?)

Example 6

hard

A car loses

15\%

of its value each year. A $20{,}000 car is worth how much after one year?

Example 7

challenge

30\%

A

equals

45\%

B

. If

A + B = 250

, find

A

and

B

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

What is

60\%

75

Example 2

hard

In a class of

32

students,

12.5\%

got an A. How many students got an A? Then find what percentage got below an A.

Example 3

easy

Find

50\%

of 40.

50% of 40 — half the bar is shaded; find the value of that half

Example 4

easy

Find

10\%

of 90.

10% of 90 — 1 out of 10 equal sections is shaded; find its value

Example 5

easy

Find

25\%

of 80.

25% of 80 — one quarter of the bar is shaded; find its value

Example 6

easy

Find

20\%

of 50.

20% of 50 — one fifth of the bar is shaded; find its value

Example 7

easy

Find

100\%

of 37.

Example 8

easy

Find

75\%

of 40.

75% of 40 — three quarters of the bar are shaded; find their value

Example 9

easy

Find

5\%

of 200.

Example 10

easy

Find

1\%

of 600.

Example 11

medium

Find

15\%

of 60.

15% of 60 — 3 out of 20 sections are shaded; find their value

Example 12

medium

12

is what percent of

48

Example 13

medium

30\%

of a number is 24. Find the number.

Example 14

medium

Find

40\%

of 250.

40% of 250 — 2 out of 5 sections are shaded; find their value

Example 15

medium

Find

150\%

of 60.

Example 16

medium

8\%

of 75 is what?

Example 17

medium

45

is what percent of

90

Example 18

medium

Find

35\%

of 80.

Example 19

medium

18

is what percent of

72

Example 20

challenge

In a class,

60\%

of 25 students passed. How many failed?

Example 21

challenge

A number increased by

20\%

becomes 96. What was the original number?

Example 22

challenge

Which is larger:

30\%

of 80, or

80\%

of 30?

Example 23

easy

Find

20\%

90

20% of 90 — one fifth of the bar is shaded; find its value

Example 24

easy

Find

25\%

120

25% of 120 — one quarter of the circle is shaded; find its value

Example 25

easy

Find

5\%

80

5% of 80 — 1 out of 20 sections is shaded; find its value

Example 26

easy

Find

200\%

35

Example 27

medium

A laptop costs $1{,}200. A tax of

7\%

is added. What is the tax amount?

Example 28

medium

60\%

\$45

is what amount?

Example 29

medium

Find

12\%

300

Example 30

medium

What is

42\%

50

Example 31

medium

40\%

of a number is

32

. Find the number.

Example 32

medium

In a school of

640

students,

55\%

ride the bus. How many ride the bus?

55% of 640 students ride the bus — 11 out of 20 sections are shaded; find the count

Example 33

medium

8\%

of a number is

20

. What is the number?

Example 34

medium

Find

125\%

48

Example 35

hard

A shirt costs $25 plus

8\%

tax. What is the total cost?

Example 36

hard

35\%

x

equals

14

. Solve for

x

Example 37

hard

A pizza shop sold

480

pizzas last week and

588

this week. What percent of last week's sales is this week's?

Example 38

hard

720

commuters,

35\%

drive alone,

25\%

carpool, and the rest take transit. How many take transit?

Example 39

challenge

After a

10\%

raise, your salary is $66{,}000. Then a

5\%

cut is taken. What is your final salary?

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Related Concepts

Percentages Decimal-Fraction Conversion Percent Change Percent Applications

Background Knowledge

These ideas may be useful before you work through the harder examples.

percentagesdecimal fraction conversion