Ratios and Percents Population Word Problem

Question

If in 9 years Town A's population rose 12% and Town B's population rose 22%, and if together the populations of Town's A and B rise by 16%. Then what was the ratio of Town A's population to Town B's population 9 years ago?

Any assistance would be appreciated.

Answer 1

Let the populations of both towns nine years ago be $A,B$ respectively.

Hence, after nine years the population of the towns becomes, $$A' = 1.12A$$ $$B' = 1.22B$$ and, $$A'+ B' = 1.16(A+B)$$ $$\therefore 1.12A + 1.22B = 1.16(A+B)$$ $$\therefore 0.04A = 0.06B$$ $$\therefore 2A = 3B$$ $$\therefore \frac{A}{B} = \frac{3}{2}$$

Answer 2

Hint:

Letting $a$ and $b$ be the initial populations of towns A and B respectively, the given information says:

$1.12a+1.22b=1.16(a+b)$

Now see what you can find out by separating the $a$ and $b$ terms in the equation.