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EXERCISE 6

Eighty percent of people in a bus are reading a newspaper. Fifteen percent are reading a novel. A person cannot be reading both.

a What is the percentage of the people in the bus who are either reading a newspaper or a novel?

b What is the percentage of the people in the bus who are neither reading a newspaper nor a novel?

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Multiplication of percentages

Multiplication of percentages arises from situations such as 55 % of class are boys and 30% of them have blue eyes. The percentage of students in the class who are boys with blue eyes is given by

30% of 55% = × = 16.5%

EXAMPLE

There are 65 000 spectators in a football stadium. 56% of the spectators barrack for the Reds. 80% of the Reds fans are male.

a Find the percentage of spectators who are male Reds supporters?

b Find the number of male Reds spectators in the stadium.

Solution

a The percentage of spectators who are male Reds supporters = 80% of 56%

= ×

= ×

=

The fraction can be converted to a percentage by multiplying by 100%

= × 100%

= %

= 44. 8%

b 44. 8% of 65 000 = × 65 000

= 29 120

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EXERCISE 7

Sixty percent of a group of people work full time. Fifteen percent of those who work full time are married. What is the percentage of people of the group who are married and work full time.

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Percentage increase and decrease

Percentage increase and decrease are discussed in the module, Clarks Women’s Sarla Cadence Closed Toe Sandals Black Grey Grey Nubuck Grey Nubuck clearance purchase under sale online 6yobsGs
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Comparing percentage change

Percentages are not only used to express change but also give us the ability to compare change.

EXAMPLE

An island has two types of rats on it.

On January 1st 2005 there were 670 Creepy rats and on January 1st 2006 the number of these rats had increased to 1260.

On January 1st 2005 there were 230 Slinky rats and on January 1st 2006 the number of these rats had increased to 659.

Find the percentage increase of the number of each type of rat.

Solution

Creepy rats increase by 1260 − 670 = 590

Percentage increase = × 100%

= %

= 88%

88.06%

Slinky rats increase by 659 − 230 = 429

Percentage increase = × 100%

= 186%

186.52%

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EXERCISE 8

City A has a population of 989 000 on January 1 2006 and a population of 1 078 000 on January 1 2008.

City B has a population of 456 000 on January 1 2006 and a population of 501 000 on January 1 2008.

Find the percentage change for each of the cities and hence state which city has the fasting growing population for the period.

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