Question

If 1/2 of the number of white mice in a certain laboratory is 1/8 of the number of the totalnumber of mice, and 1/3 of the number of gray mice is 1/9 of the total number of mice, then whatis the ratio of the number of white mice to the number of gray mice?

Answer 1

Let there are w white mice, g be gray mice and t be total number of mice.

The equation for white mice and total number of mice is,

$\begin{gathered} \frac{w}{2}=\frac{t}{8} \\ w=\frac{t}{4} \\ 4w=t \end{gathered}$

The equation for gray mice and total number of mice is,

$\begin{gathered} \frac{g}{3}=\frac{1}{9}t \\ g=\frac{t}{3} \\ 3g=t \end{gathered}$

Divide both the equation to determine the ratio of the number of white mice to the number of gray mice.

$\begin{gathered} \frac{4w}{3g}=\frac{t}{t} \\ \frac{4w}{3g}=1 \\ \frac{w}{g}=\frac{3}{4} \end{gathered}$

So the ratio of the number of white mice to the number of gray mice is 3/4.

Answer: 3/4