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11.2 Comparing different quantities

11.2 Comparing different quantities

You will o"en need to compare groups that are di$erent sizes.
Suppose that, in one school, 85 students took an exam and 59 passed.
In another school, 237 students took an exam and 147 passed.

Which school did better? It is hard to say because each school had a di$erent number of students.
!e worked example shows how to use percentages to help to answer questions like this.

Worked example 11.2

In school A, 85 students took a mathematics exam and 59 passed.
In school B, 237 students took a mathematics exam and 147 passed.
Which school had a better pass rate?

59 out of 85 = 59 ÷ 85 = 69% 59 ÷ 85 = 0.694… = 69% to the nearest
whole number.
147 out of 237 = 147 ÷ 237 = 62% 147 ÷ 237 = 0.620… = 62% to the
nearest whole number.
The pass rate in school B is better by seven percentage points. The difference between 62% and 69% is
given in ‘percentage points’.

) Exercise 11.2

1 There were 270 people in a cinema. There were 168 women and The venue is the place where
102 men. something happens. In this case
There were 152 people in a theatre. There were 78 women it is the cinema or the theatre.
and 74 men.
a Work out the percentage of women in each venue.
b Work out the percentage of men in each venue.

2 There are 425 girls and 381 boys in a school. 31 girls and 48 boys are overweight.
a Work out the percentage of the girls that are overweight.
b Work out the percentage of the boys that are overweight.
c Work out the percentage of all the students that are overweight.

3 In Alphatown there are 5400 young people aged 18 or less. There are 9300 aged over 18.
In Betatown there are 9300 young people aged 18 or less. There are 21 600 aged over 18.
a Calculate the percentage of young people in each town.
b Which town has the greater proportion of young people?
4 This table shows the results of a survey in a factory. Smoker Non-smoker Total
a What percentage of men are smokers? Men 12 64 76
b Compare the percentages of men and women who Women 9 32 41
are non-smokers.
5 This table shows the ages of cars owned by Age of car Less than 5 years 5 years or more
two groups of people. Engineers 34 53
Use percentages to compare the ages of cars Accountants 41 102
owned by engineers and by accountants.

11 Percentages 105