Percentages 3
Quantities as Percentages

To answer questions such as,

In a test, is it better to score 30 out of 40 or 40 out of 50?

it is helpful to express the scores as percentages.

Worked Examples

1

Express '30 out of 40' and '40 out of 50' as percentages. Which is the higher score?

Show me

'30 out of 40' can be written as and '40 out of 50' can be written as .

Changing these fractions to percentages,

= × 100% and = × 100%
= 75% = 80%

So '40 out of 50' is the higher score, since 80% is greater than 75%.
2

A student scores 6 out of 10 in a test. Express this as a percentage.

Show me

'6 out of 10' can be written as . Changing this fraction to a percentage,

= × 100% = 60%
3

Robyn and Rachel bought a DVD for £20. Robyn paid £11 and Rachel paid £9. What percentage of the total cost did each girl pay?

Show me

Robyn paid £11 out of £20, which is

= × 100% = 55%

Rachel paid £9 out of £20, which is

= × 100% = 45%
4

David earns £200 per week and saves £15 towards the cost of a mobile phone. What percentage of his earnings does he save?

Show me

He saves £15 out of £200, which is

= × 100% = 7.5%

Exercises

Express each of the following as percentages.

(a)
8 out of 50 %
(b)
3 out of 25 %
(c)
8 out of 20 %
(d)
3 out of 10 %
(e)
6 out of 50 %
(f)
6 out of 40 %
(g)
12 out of 80 %
(h)
9 out of 30 %
(i)
27 out of 30 %
(j)
120 out of 300 %
(k)
84 out of 200 %
(l)
260 out of 400 %
(m)
28 out of 70 %
(n)
18 out of 60 %
(o)
51 out of 60 %

In a class of 25 students there are 10 girls. What percentage of the class are girls and what percentage are boys?

% of the class are girls and % are boys.

In the USA, the price of a bar of chocolate is 25 cents and includes 5 cents profit. Express the profit as a percentage of the price.

%

The value of a house is £40 000 and the value of the contents is £3200. Express the contents value as a percentage of the house value.

%

In the crowd at a cricket match between Jamaica and Trinidad there were 14 000 Jamaica supporters and 11 000 Trinidad supporters. What percentage of the crowd supported each team?

% Jamaica supporters and % Trinidad supporters.

Adrian finds that in a delivery of 500 bricks there are 20 broken bricks. What percentage of the bricks are broken?

%

A glass of drink contains 50 ml of fruit juice and 200 ml of lemonade. What percentage of the drink is lemonade?

%

Two recipes for making chocolate drinks are shown in the table below.

Cups of MilkCups of Chocolate
Recipe A32
Recipe B21
(a)

What percent of the mixture using Recipe A is chocolate?

%
(b)

By showing suitable calculations, determine which of the two recipes, A or B, is richer in chocolate.

(c)

If the mixtures from Recipe A and Recipe B are combined, what is the percent of chocolate in the new mixture?

%
(d)

A vendor makes chocolate drink using Recipe A. 3 cups of milk and 2 cups of chocolate can make 6 bottles of chocolate drink. A cup of milk costs £0.70 and a cup of chocolate costs £1.15.

(i)

What is the cost of making 150 bottles of chocolate drink?

£
(ii)

What should be the selling price of each bottle of chocolate drink to make an overall profit of 20%?

£

Investigation

The ancient Egyptians were the first to use fractions. However, they only used fractions with a numerator of one. Thus they wrote as + , etc.
What do you think the Egyptians would write for the fractions , , and ?