Answer:
[tex]\frac{8}{17}[/tex] 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,
[tex]\frac{3}{4}\text{ of } x=\frac{2}{3}\text{ of }y[/tex]
[tex]\frac{3x}{4}=\frac{2y}{3}[/tex]
By cross multiplication,
[tex]9x=8y[/tex]
[tex]\implies \frac{x}{y}=\frac{8}{9}[/tex]
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 = [tex]\frac{\text{Guppies}}{\text{Total fishes}}[/tex]
[tex]=\frac{8x}{17x}[/tex]
[tex]=\frac{8}{17}[/tex]
