# The population of town A increases from 1,346 to 1,500. In the same period, the population of town B increases from 1,546 to 1,800. What is the percent increase in population for town A and for town B? Which town had the greater percent of increase?

Sep 26, 2017

Town A had a percentage increase of 11.4% (1.d.p) and Town B had a percentage increase of 16.4%.

Town B had the greatest percentage increase because 16.429495472 % > 11.441307578 %.

#### Explanation:

First, let's delve into what a percent actually is. A percentage is a specific amount per hundred (cent).

Next, I'll show you how to calculate the percentage increase. We have to first calculate the difference between the new number and the original number. The reason why we compare these is because we are finding how much a value has changed.

Increase = New number - Original number

To calculate the percentage increase we have to do the increase divided by the original number. This gives us the increase, but as a decimal, so we have to multiply the decimal by a hundred to give us a percentage.

% Increase = (Increase ÷ Original number) × 100

So let's get on to the question.

Town A

First, we have to find the increase.

$I n c r e a s e = 1500 - 1346$

Increase = color(green)(154

Now let's divide the increase by the original number.

$\frac{154}{1346} = 0.11441307578$

Finally the percentage increase is...

0.11441307578 xx 100 = color(green)(11.441307578%

Town B

Again, we have to find the increase.

$I n c r e a s e = 1800 - 1546$

Increase = color(green)(254

Let's divide by the original number.

$\frac{254}{1546} = 0.16429495472$

Next, let's multiply it by a hundred.

0.16429495472 xx 100 = color(green)(16.429495472 %)

Which one had the greatest percentage increase?

Town A = 11.441307578 %

Town B = 16.429495472 %

Town B had the greatest percentage increase because 16.429495472 % > 11.441307578 %.