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

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

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New post 21 Nov 2019, 01:04
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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) \(\frac{8}{9}\)
Spoiler: OA

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

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

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New post 21 Nov 2019, 10:50
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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
Answer is b.

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

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New post 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.

Answer: B
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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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