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} (w)/(2)=(t)/(8) \\ w=(t)/(4) \\ 4w=t \end{gathered}`

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

`\begin{gathered} (g)/(3)=(1)/(9)t \\ g=(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} (4w)/(3g)=(t)/(t) \\ (4w)/(3g)=1 \\ (w)/(g)=(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