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?
Accepted Solution
A:
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 : 9Let guppies = 8x, swordtail = 9xWhere, x is any number,Since, the aquarium contains only two kinds of fish, guppies and swordtails,So, the total fishes = 8x + 9x = 17xHence, 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]