# AN 8% INCREASE IN POPULATION EQUALS 1998 PEOPLE SO WHAT WAS PREVIOUSE POPULATION? I KNOW THE ANSWER IS 1850, BUT I NEED TO SEE HOW THEY GOT THIS ANSWER

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You need to convert the request of the problem into an equation, where population represents the variabl, hence, you should come up with the substitution for previous population P.

The problem provides the information that an increase of population of `8%` gives `1998` people, hence, you may write the following equation:

`P + 0.08 P = 1998`

Notice that `0.08 P` represents the increase of population by 8 percents.

`1.08P = 1998 => P = 1998/1.08 => P = 1850`

**Hence, evaluating the previous population yields **`P = 1850.`

Just write what the sentence is asking for in math language: what number when increased by 8% of itself is 1998.

So for what number, write x. Then for increased by 8% of itself, that's plus +, eight percent of x, so 0.08x, so write + 0.08x. Finally, equals 1998 is of course = 1998.

so put it together, and you have

x + 0.08x = 1998 --then just solve for x:

1.08x=1998

x= 1998 / 1.08

x= 1850

8% increase of previous population + previous population=1998

i.e(1 + 8/100) of Pre.Popun= 1998

Therefore, Pre. popun = (1998 x 100)/108 = 1850