Home > Pre-Algebra > Percentages > Percentage Increase

## Percentage Increase

#### Introduction

Percentage is a scale used to compare items of different values. A percentage measures everything on the same scale, from 0 to 100. Something that is half the size of something else can be said to be 50% of the size.

If we buy tickets for a concert every year for $100, and find out that the ticket price has gone up 10%, we can quickly and easily calculate what the actual price is. If another concert sells tickets for$80 but has put their price up 20%, we can compare which of the two is cheaper.

## Lesson

To calculate percentage increase, we can use the percentage to work out the actual increase. The steps we need to follow are:

1) Calculate the actual increase by using the percentage

2) Add this amount back on to the original amount to find the new price

Using the examples of the concerts above:

The first concert used to sell tickets for $100 but has put them up 10% this year. Firstly, we need to work out 10% of$100. To do this, we need to turn 10% into a decimal. To turn any percentage into a decimal, we take the percentage number and divide by 100.

So, $10 ÷ 100 = 0.1$

Now, to work out 10% of $100, we multiply the$100 by 0.1:

$\100 x 0.1 = \10.$

Therefore, the cost of the ticket has increased by $10. We can then add that back on to the cost of the original ticket to work out the new price:$100 (original cost) + $10 (the increase) =$110 (the new price).

Let's try that again with the ticket for the other concert. Their old price was $80 and they have raised the cost by 20%. Firstly, we turn 20% into a decimal by diving 20 by 100. $20 ÷ 100 = 0.2$ Then, we multiply the old cost ($80) by 0.2:

$\80 x 0.2 = \16$

So, the price increase is $16. We can then add that back on to the original price to work out the new price:$80 (original cost) + $16 (the increase) =$96 (the new price).

Therefore, the second concert is still cheaper, despite the percentage increase being higher.

## Examples

Carter saw a book he wanted on Amazon for \$21. The next day he noticed that the price had increased to \$31. By what percent did the price increase?
First, find the number of dollars the price increased
$31 - 21 = 10$
To find what percentage 10 is of 21, we need to divide
$\dfrac{10}{21} = 0.476$
Moving the decimal place two to the right and then putting a % sign at the end of the number we get:
$0.476$ = KaTeX parse error: Expected 'EOF', got '%' at position 5: 47.6%̲