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11.3 Percentage changes

11.3 Percentage changes

You can use percentages to describe a change in a quantity. It could be an increase or a decrease.
A percentage change is always calculated as a percentage of the initial value.

!e initial value is 100%. It is important to choose the correct value to be 100%.
Worked example 11.3

In May 800 people visited a museum. In June 900 people visited. In July, the number was 800 again.
Work out:
a the percentage increase from May to June b the percentage decrease from June to July.

a 100% = 800 The initial value in May.
The increase is 100. 900 – 800
1
The percentage increase is 100 × 100 = 12.5%. The fraction 100 simplifi es to .
800 800 8 The percentages
b 100% = 900 The initial value is 900 this time. are not the same.
The decrease is 100. A decrease from 900 to 800
100
1
The percentage decrease is 900 × 100 = 11.1%. The fraction 100 simplifi es to .
9
900
) Exercise 11.3

1 Here are the prices of three items in Alain’s shop.
Game $40 Phone $120 Computer $500
Alain increases all the prices by $10. Find the percentage increase for each item.

2 These are the masses of three children one April.
Luke 6 kg Bridget 14 kg Tomas 25 kg
Over a year, the mass of each of them increased by 10%. Work out the new mass of each child.

3 a One week the height of a plant increased from 30 cm to 35 cm. Work out the percentage increase.
b The following week the height increased by 12%. Work out the new height.

4 Tebor weighed 84 kg. He went running every day and began to lose mass.
After one month his mass was 78 kg. What was the percentage decrease?
5 a The speed of a car increased from 90 km/h to 120 km/h. What is the percentage increase?
b Here are some more changes of speed. Write each one as a percentage.
i from 40 km/h to 55 km/h ii from 55 km/h to 70 km/h iii from 70 km/h to 40 km/h.
6 The price of a car was $20 000. In a sale, the price decreased
by 4%. After the sale it increased by 4%.
a What mistake has Ahmad made? The price after the sale
b What is the correct price after the sale? is $20 000 again.

A statistician noted the population of her country in three different years.
7 A statistician noted the population of her country in three different years.
1900: 4.6 million 1950: 7.2 million 2000: 13.8 million
Find the percentage increase:
a from 1900 to 1950 b from 1950 to 2000 c from 1900 to 2000.

106 11 Percentages