Question

A large aquarium contains only two kinds of fish, guppies and swordtails. If 3/4​​ of the number of guppies is equal to 2/3​​ of the number of swordtails, then what fraction of fish in this aquarium are guppies?

Answer 1

Answer:

$\frac{8}{17}$ of fish in this aquarium are guppies.

Step-by-step explanation:

Let x be the number of guppies and y be the number of swordtails in the aquarium,

According to the question,

$\frac{3}{4}\text{ of } x=\frac{2}{3}\text{ of }y$

$\frac{3x}{4}=\frac{2y}{3}$

By cross multiplication,

$9x=8y$

$\implies \frac{x}{y}=\frac{8}{9}$

Thus, the ratio of guppies and swordtail fishes is 8 : 9

Let guppies = 8x, swordtail = 9x

Where, x is any number,

Since, the aquarium contains only two kinds of fish, guppies and swordtails,

So, the total fishes = 8x + 9x = 17x

Hence, the fraction of fish in the aquarium are guppies = $\frac{\text{Guppies}}{\text{Total fishes}}$

$=\frac{8x}{17x}$

$=\frac{8}{17}$