11.3 Percentage Changes

You can use percentages to describe a change in a quantity. It could be a decrease or an increase. A percentage is always calculated as a percentage of the initial value. The initial value is 100%. It's important to choose the correct value to be 100%. I have three questions to ease your understanding.

Question

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.

Game: The initial value is 40. So 10/40*100% = 25%
Phone: The initial value is 120. So 10/120*100% = 8,3%
Computer: The initial value is 500. So 10/500*100%

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

Luke: 6*110% = 6,6 
Bridget: 14*110% = 15,4
Thomas: 25*110% = 27,5

3. The price of a car was $20000. In a sale, the price decreased by 4%. After the sale it increased by 4%.
Ahmad says "The price after the sale is 20000 again"
a. What mistake has Ahmad made?
b. What is the correct price after the sale?

a) He misplace the initial value for the price after sale. The first initial value is 20000. the second initial value is 19200. So the result won't be the same as before.

b) 19200*104% = 19968