# EXPRESS ONE QUANTITY AS A PERCENTAGE OF ANOTHER WORD PROBLEMS

To express one quantity as a percentage of another, we follow the steps given below.

Step 1 :

Write the given quantities as fraction.

Step 2 :

To convert a fraction or decimal to percentage, we have to multiply by 100%.

Problem 1 :

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

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

(b) 1000 students attend Hightown School. How many girls attend Hightown School?

Solution :

Total number of students = 50

Number of girls = 29

a)  Percentage of girls = (29/50) x 100%

= (29 x 2)%

= 58%

b) Number of students attend in Hightown school = 1000

= 58% of 1000

= 0.58 x 1000

= 580

So, total number of girls in total of 1000 students is 580.

Another way :

= (29/50)

Express the denominator 50 as 1000, then multiplying by 100% we can convert as percentage.

= (29/50) x (20/20)

= 580/1000

So, total of 1000 students 580 students are girls.

Problem 2 :

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

Solution :

Amount David receives = \$5

Amount he is giving to his sister = \$2

Expressing it as percentage = (2/5) x 100%

= 2 x 20%

= 40%

So, 40% of money he gives to his sister.

Problem 3 :

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

Solution :

Total number of questions in the quiz = 8

Number question he did correctly = 6

Expressing it as percentage = (6/8) x 100%

= 75%

So, he scores 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 :

Total number of flapjacks he brings = 500

Number of flapjacks he sells = 450

Percentage of flapjacks he sells = (450/500) x 100%

= (450/5)%

= 90%

Problem 5 :

Write 94 out of 200 as a percentage

Solution :

Total marks = 200

She has received = 94

Percentage of marks = (94/200) x 100%

= (94/2) %

= 47 %

Problem 6 :

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

Solution :

Total score = 20

Collin's score = 13

Expressing into fraction = 13/20

Expressing it 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 at match = 222

Writing 222 out of 600 as a 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

He deposits = \$6000

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

= (6/15) x 100%

= 40%

So, 40% of the amount he is paying as deposit.

Problem 9 :

There are 400 beads in a bag. 140 of the 400 beads are yellow. Work out 140 as a percentage of 400

Solution :

Total number of beads = 400

Number of yellow beads = 140

Expressing it as percentage of yellow beads

= (140/400) x 100%

= 35%

Problem 10 :

James scored 30 out of 90 in a music test. He scored 48 out of 150 in a drama test. James scored 35 out of 120 in an art test. In which test did James score the highest percentage? You must show your workings

Solution :

Percentage in music test :

= (30/90) x 100%

= 33.3%

Percentage in drama test :

= (48/150) x 100%

= 32%

Percentage in art test :

= (35/120) x 100%

= 29.1%

Observing the above percentages, in music test he got high score.

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