Question

There are a total of 255 dogs, cats, fish in a pet store. The ratio of dogs to cats is 3:5 and ratio of cats to fish is 2:7. How many fish are in the pet store?

Answer 1

Let the number of cats be c, the number of dogs be d and the number of fish be f.
\[\frac{d}{c}=\frac{3}{5}\]
Therefore
\[d=\frac{3}{5}c\ ........(1)\]
Also
\[\frac{c}{f}=\frac{2}{7}\]
Therefore
\[f=\frac{7}{2}c\ ...........(2)\]
Equations (1) and (2) give the numbers of dogs and fish in terms of the number of cats.
\[c+d+f=255\ ...........(3)\]
Plugging in the expressions for d and f from equations (1) and (2) into equation (3) we get
\[c+\frac{3}{5}c+\frac{7}{2}c=255\ ........(4)\]
Now you can use equation (4) to find the number of cats, and then by substitution into equation (2) the number of fish can be found.

Answer 2

Thank you so much~

Answer 3

You're welcome :)