The 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]
The percentage increase is:
100 / 800 x 100 = 12.5% [the fraction 100/800 simplifies to 1/8]
b. 100% = 900 [the initial value is 900 this time]
The decrease is 100 [a decrease from 900 to 800]
The percentage decrease is:
100 / 900 x 100 = 11.1% [the fraction 100/900 simplifies to 1/9]
*the percentages are NOT the same.
Here are more examples about percentage changes:
Question 1:
The price of a car was $20 000. In sale, the price decreased by 4%. After the sale it increased by 4%.
Ahmad:"The price after the sale is $20 000 again"
a. What mistake has Ahmad made?
answer:
We must first solve the question before going to Ahmad's mistake.
Decrease:
= $20 000 - (4/100 x 20 000)
= $20 000 - $800
= $19 200
Increase:
= $19 200+ (4/100 x 19 200)
= $19 200 + $768
= $19 968
Ahmad is incorrect because he answered $20 000 instead of $19 968
b. What is the correct price after the sale?
From what I have counted above, the correct price is $19 968
Question 2:
One week the height of a plant increased from 30 cm to 35 cm.
a. Work out the percentage increase.
answer:
35 - 30 = 5
5/30 x 100 = 17% (rounded off to the nearest whole number)
The increase percentage is 17%
The following week the height increase by 12%.
b. Work out the new height.
answer:
12/100 x 35 = 4.2 cm
4.2 cm + 35 cm
= 39.2 cm
Here is a video about this subchapter.
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