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An SPCA shelter has only cats and dogs, and one third of the animals

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Bunuel
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An SPCA shelter has only cats and dogs, and one third of the animals [#permalink] New post   30 Jun 2021, 04:15
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An SPCA shelter has only cats and dogs, and one third of the animals are cats. If 2 cats were adopted from the SPCA shelter and 5 dogs brought to the SPCA shelter, then the ratio of cats to dogs would be 3:7. How many cats are in the shelter?

A. 23
B. 26
C. 29
D. 31
E. 34
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IanStewart
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Re: An SPCA shelter has only cats and dogs, and one third of the animals [#permalink] New post   30 Jun 2021, 10:07
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When we remove 2 cats, the ratio of cats to dogs becomes 3 to 7. So when we subtract 2 from the number of cats, we must get a multiple of 3, and only A, B or C is possible.

After we remove 2 cats and add 5 dogs, the total number of animals increases by 3, and the ratio becomes 3 to 7, so the total becomes a multiple of 10, so ends in zero. That means the total before the changes must end in 7. But the total before the changes is just 3 times the right answer, since the number of cats is 1/3 of the total. Only 29 gives us a units digit of 7 when we multiply by 3, so it must be correct.
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Re: An SPCA shelter has only cats and dogs, and one third of the animals [#permalink] New post   30 Jun 2021, 22:18
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if c = 1/3 of total animals then d are 2/3rd so ratio of c:d = 1:2 hence d =2c

now c-2 / d+5 = 3/7. replace d as 2c and the answer is 29
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Re: An SPCA shelter has only cats and dogs, and one third of the animals [#permalink] New post   30 Jun 2021, 23:33
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Bunuel wrote:
An SPCA shelter has only cats and dogs, and one third of the animals are cats. If 2 cats were adopted from the SPCA shelter and 5 dogs brought to the SPCA shelter, then the ratio of cats to dogs would be 3:7. How many cats are in the shelter?

A. 23
B. 26
C. 29
D. 31
E. 34


Cats are 1/3rd so dogs will be 2/3rd.
So if there are n cats, there will be 2n dogs.

\(\frac{(n-2)}{(2n + 5)} = \frac{3}{7}\)
n = 29

Answer (C)
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Re: An SPCA shelter has only cats and dogs, and one third of the animals [#permalink] New post   24 Aug 2022, 12:09
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Re: An SPCA shelter has only cats and dogs, and one third of the animals [#permalink]
24 Aug 2022, 12:09
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