After a 5% increase...?

Question

After a 5% increase, the population of a city is 117000. What was the former population?

Any help is appreciated and if possible could you show work because I tried numerous times and got it wrong.

Answer 1

117,000/1.05 = 111429

Answer 2

To add a percentage to a number, you multiply it by 1.NN Where NN is the percentage (i.e. 05 for 5%)

So if we multiply to get to 117000, then we must divide to return.

Initial population = 117000/1.05

Initial population = 111428.57

This number clearly makes no sense so we must round off the number.

The initial population would therefore be 111429 which is an increase in population of 4.9999%

Answer 3

If you want to understand it, read below.

Let the former population be x

The new population is (100%+5%)x = 105% x = 1.05x

and this 1.05x equals the given number 117000, therefore:

1.05x = 117000

Now solve for x (former population):

x = 117000/1.05 = 111429