EXPRESSING A NUMBER AS A PERCENTAGE OF ANOTHER

Problem 1 :

For every 50 students at Hightown School, 29 are girls.

(a) Work out 29 as a percentage of 50.

1000 students attend Hightown School.

(b) How many girls attend Hightown School?

Solution :

(a) Total number of students = 50, number of girls = 29

Expressing it as percentage = 29/50 (Out of 50, 29 are girls)

To convert 50 as 1000, we will multiply 50 by 20, so the numerator also be multiplied by 20. We get

= (29/50) ⋅ (20/20)

= 580/1000

So, 580 girls are there.

Problem 2 :

David receives $5 from his Grandmother. He gives $2 to his sister. Write down $2 as a percentage of $5.

Solution :

Money received from his grand mother = $5

Amount given to his sister = $2

Expressing it as percentage, we get

= (2/5) ⋅ 100%

= 40%

Problem 3 :

Roger scores 6 out of 8 in a quiz. Work out his score as a percentage.

Solution :

Total score = 8, He has scored = 6

Expressing it as percentage,

= (6/8) ⋅ 100%

= 75%

Problem 4 :

Susan brings 500 flapjacks to a local fair. Susan sells 450 of the flapjacks. What percentage of the flapjacks did Susan sell?

Solution :

Number of flapjacks = 500

Number of flapjack he sells = 450

Expressing it as percentage = (450/500) x 100%

= 90%

Problem 5 :

Write 94 out of 200 as a percentage.

Solution :

94 out of 200 = (90/200)

Expressing it as percentage = (90/200) x 100%

= 45%

Problem 6 :

Colin gains 13 out of 20 in a class test. Work out his mark as a percentage.

Solution :

Total score = 20

Collin gains = 13

Expressing as fraction = 13/20

Expressing as percentage = (13/20) x 100%

= (13 x 5) %

= 65%

Problem 7 :

There are 600 people at a football match. There 222 children at the match. Write 222 out of 600 as a percentage.

Solution :

Total number of people = 600

Number of children in the match = 222

Expressing as fraction, we get

= (222/600)

Expressing as percentage = (222/600) x 100%

= 37%

Problem 8 :

Bryan buys a car costing $15000. He pays a deposit $6000. What is $6000 as a percentage of $15000?

Solution :

Cost of car = $15000

Deposit = $6000

Expressing as percentage = (6000/15000) x 100%

= 40%

Problem 9 :

The price of a cinema ticket is reduced from $8 to $7.50 Calculate the reduction as a percentage of the original price

Solution :

Price of ticket = $8

Price of ticket after reduction = $7.50

Difference in price = 8 - 7.50

= 0.50

Expressing the reduction as percentage of original price

= (0.50/8) x 100%

= 6.25%

Problem 10 :

The population of a country is 2.85 x 10⁶. The number of people that own a rabbit is 1.24 x 10⁵. Calculate the percentage of the population that own a rabbit.

Solution :

Total population = 2.85 x 10⁶

People that own rabbit = 1.24 x 10⁵

Percentage of population that own rabbit

= (1.24 x 10⁵)/(2.85 x 10⁶) x 100%

= (124000/2850000) x 100%

= 4.35%

Problem 11 :

The width of a rectangular room is 80% of its length. What is the area of the room?

Solution :

Length of rectangular room = 15 ft

Width = 80% of length

= 80/100 of 150

= 0.80(15)

= 12 ft

Area of rectangular room = length x width

= 12 x 15

= 180 square ft

Problem 12 :

Lake Worth, near West Palm Beach, had about 2120 acres of mangrove trees 40 years ago. Only about 13% of the mangrove trees remain. How many acres of mangrove trees remain?

Solution :

Area of mangrove trees = 2120 

13% of mangrove trees remain = 13% of 2120

= 13/100 x 2120

= 0.13 (2120)

= 275.6

approximately 276 acres.

Problem 13 :

The price of a bicycle after a 25% discount is $679.99. What was the original price? Round to the nearest cent.

Solution :

Let x be the original price of bicycle.

After reducing 25%, we get 75% of the original price = 679.99

0.75 of x = 679.99

0.75x = 679.99

x = 679.99/0.75

= 906.65

So, original price of the bicycle is $907 approximately.

Problem 14 :

After a tune up a car produced 5% more horsepower. If the horsepower after the tune up is 525, what was the horsepower before the tune up?

Solution :

Let x be 100% of the horsepower before tue up.

105% of x = 525

1.05 x = 525

x = 525/1.05

x = 500

At the beginning the quantity of horse power is 500.

Problem 15 :

The new model of a car is 12% cheaper than the previous model. If the current model costs $56300, what was the price of the previous model? Round to the nearest cent.

Solution :

Let x be the original price of the precious model

(100 - 12)% of x = 56300

88% of x = 56300

0.86x = 56300

x = 56300/0.86

x = 65465

So, the original price of the model is $65465.

Problem 16 :

After a 7% raise in weekly salary, Matt is now making $1450 per week. What was Matt’s weekly salary before the raise? Round to the nearest cent.

Solution :

Let x be the original salary.

Salary per week now = 107% of x

107% of x = 1450

1.07x = 1450

x = 1450/1.07

x = 1355.14

So, before raise he may recieve $1355.1 approximately.