SOLVING WORD PROBLEMS ON PERCENTAGE

Problem 1 :

A student answered 86 problems on a test correctly and received a grade 98%. How many problems were on the test, if all the problems were worth the same number of points? (Round to the nearest whole number)

Solution :

Number of questions he answered correctly = 86

Let x be the total number of questions.

98% of x = 86

0.98(x) = 86

Dividing by 0.98 on both sides.

x = 86/0.98

x = 87.75

x = 88

So, there are 88 problems.

Problem 2 :

Manuel found a wrecked Trans-Am that he could fix. He bought the car for 65% of the original price of $7200. What did he pay for the car? (Round to nearest dollar)

Solution :

Original price of the car = $7200

= 65% of 7200

= 0.65 (7200)

= 4680

He paid $4680 for the car.

Problem 3 :

Pamela bought an electric drill at 85% of the regular price. She paid $32.89 for the drill. What was the regular price? (Round to the nearest cent)

Solution :

Let x be the regular price.

85% of x = 32.89

0.85x = 32.89

Dividing by 0.85 on both sides.

x = 32.89/0.85

x = 38.69

Problem 4 :

A crew is made up of 8 men, the rest are women. 66  2/3 % of the crew are men. How many people are in the crew?

Solution :

Let x be the number of women in the crew.

Total number people (crew) = 8 + x

66  2/3% of (8 + x) = 8

200/3% of (8 + x) = 8

0.66(8 + x) = 8

5.28 + 0.66x = 8

0.66x = 8 - 5.28

0.66x = 2.72

Dividing by 0.66 on both sides.

x = 2.72/0.66

x = 4.12

So, total number of girls in the crew is 4.

Total member in the crew = 8 + 4

= 12 people are in the crew.

Problem 5 :

Ben earns $12,800 a year. About 15% is taken out for taxes. How much is taken out for taxes?

Solution :

His earning = $12800

15% of the earnings taken for tax.

= 15% of 12800

= 0.15 (12800)

= 1920

So, the tax amount is $1920.

Problem 6 :

At a sale, shirts were sold for $15 each. This price was 80% of their original price. What was the original price?

Solution :

Let x be the original price.

Selling price of shirt = $15

80% of x = 15

0.80x = 15

Dividing by 0.80 on both sides.

x = 15/0.80

x = 18.75

So, the original price is $18.75.

Problem 7 :

There are 32 students in a class. Nine of those students are women. What percent are men? (round to the nearest tenth)

Solution :

Total number of students = 32

Number of students are women = 9

Percentage of women = (9/32) x 100%

= 28.12%

= 28%

Percentage of women = 100 - 28

= 72%

Problem 8 :

The Royals softball team played 75 games and won 55 of them. What percent of the games did they lose? (round to the nearest tenth)

Solution :

Total number of games = 75

Number of games he won = 55

Number of games he lose = 75 - 55

= 20

Number of games he lose = (20/75) x 100%

= 26.6 %

So, 27% of the game they lost.

Problem 9 :

In a survey, a group of students were asked their favorite sport. “Other” sports were chosen by 18 people.

a. How many students participated?

b. How many chose football?

Solution :

a)

Let x be the total number of students.

Other = 100% - (40 + 37.5)%

= (100 - 77.5)%

= 22.5%

22.5% of x = 18

(22.5/100)·x = 18

x = 18 (100/22.5)

x = 1800/22.5

x = 80

So, total number of students is 80.

b) Percentage of students choose foot ball = 37.5%

= (37.5/100) of 80

= 0.375(80)

= 30

So, 30 students choose football.

Problem 10 :

Describe and correct the error in using the percent proportion to answer the question below. “40% of what number is 34?”

Solution :

Let a be the required number.

40% of a = 34

(40/100) · a = 34

a/34 = 100/40

a = 100(34)/40

a = 85

Problem 11 :

Of 140 seventh-grade students, 15% earn the Presidential Physical Fitness Award. How many students earn the award?

Solution :

Total number of students = 140

Number of students earn Presidential Physical Fitness Award = 15% of 140

= (15/100) · 140

= 0.15(140)

= 21

So, the number of students is 21.

Problem 12 :

A salesperson receives a 3% commission on sales. The salesperson receives $180 in commission. What is the amount of sales?

Solution :

Commission = $180

= 3% of commission on sales 

= 3% of 180

= (3/100) · 180

= (3 · 180)/100

= $5.4