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# A large aquarium contains only two kinds of fish, guppies, and swordta

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Math Expert
Joined: 02 Sep 2009
Posts: 59622
A large aquarium contains only two kinds of fish, guppies, and swordta  [#permalink]

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21 Nov 2019, 01:04
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Difficulty:

35% (medium)

Question Stats:

81% (01:40) correct 19% (01:30) wrong based on 37 sessions

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

(A) $$\frac{5}{12}$$

(B) $$\frac{8}{17}$$

(C) $$\frac{9}{17}$$

(D) $$\frac{7}{12}$$

(E) $$\frac{8}{9}$$

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Re: A large aquarium contains only two kinds of fish, guppies, and swordta  [#permalink]

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21 Nov 2019, 03:30
3/4 *G= 2/3*S
G/S = 8/9
8/17
IMO B

Bunuel wrote:
A large aquarium contains only two kinds of fish, guppies, and swordtails. If $$\frac{3}{4}$$ of the number of guppies is equal to $$\frac{2}{3}$$ of the number of swordtails, then what fraction of fish in this aquarium are guppies?

(A) $$\frac{5}{12}$$

(B) $$\frac{8}{17}$$

(C) $$\frac{9}{17}$$

(D) $$\frac{7}{12}$$

(E) $$\frac{8}{9}$$
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Joined: 16 Feb 2015
Posts: 130
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Concentration: Finance, Operations
A large aquarium contains only two kinds of fish, guppies, and swordta  [#permalink]

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21 Nov 2019, 10:50
1
Bunuel wrote:
A large aquarium contains only two kinds of fish, guppies, and swordtails. If $$\frac{3}{4}$$ of the number of guppies is equal to $$\frac{2}{3}$$ of the number of swordtails, then what fraction of fish in this aquarium are guppies?

(A) $$\frac{5}{12}$$

(B) $$\frac{8}{17}$$

(C) $$\frac{9}{17}$$

(D) $$\frac{7}{12}$$

(E) $$\frac{8}{9}$$

Explanation: let, Guppies =a, Swordtails=b
3/4 of Guppies = 2/3 of Swordtails
so (3/4)a=(2/3)b... solving this we get 9a=8b; a/b=8/9
By ratio proportionate:
a/(a+b) = 8/(9+8)= 8/17

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Re: A large aquarium contains only two kinds of fish, guppies, and swordta  [#permalink]

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24 Nov 2019, 07:22
Bunuel wrote:
A large aquarium contains only two kinds of fish, guppies, and swordtails. If $$\frac{3}{4}$$ of the number of guppies is equal to $$\frac{2}{3}$$ of the number of swordtails, then what fraction of fish in this aquarium are guppies?

(A) $$\frac{5}{12}$$

(B) $$\frac{8}{17}$$

(C) $$\frac{9}{17}$$

(D) $$\frac{7}{12}$$

(E) $$\frac{8}{9}$$

We can create the equation:

3G/4 = 2S/3

9G = 8S

We can let G = 8 and S = 9.

Thus, guppies are 8/17 of the total fish at the aquarium.

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Re: A large aquarium contains only two kinds of fish, guppies, and swordta   [#permalink] 24 Nov 2019, 07:22
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