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In a certain animal shelter, the ratio of the number of dogs to the nu

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In a certain animal shelter, the ratio of the number of dogs to the nu  [#permalink]

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New post 12 Sep 2015, 12:24
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In a certain animal shelter, the ratio of the number of dogs to the number of cats is 15 to 7. If 12 additional cats were to be taken in by the shelter, the ratio of the number of dogs to the number of cats would be 15 to 11. How many dogs are in the shelter?

A. 15
B. 25
C. 30
D. 45
E. 60

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Re: In a certain animal shelter, the ratio of the number of dogs to the nu  [#permalink]

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New post 12 Sep 2015, 16:20
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Hi shasadou,

This ratio question can be solved in a couple of different ways. Here's an Algebraic approach...

We're told that the ratio of the number of dogs to the number of cats is 15:7. We're then told that 12 more cats are added to this group and the ratio becomes 15:11. We're asked for the number of dogs.

Algebraically, since the number of dogs is a multiple of 15 and the number of cats is a multiple of 7, we can write this initial relationship as...

15X/7X

When we add the 12 cats and factor in the 'ending ratio', we have an equation....

15X/(7X+12) = 15/11

Here we have 1 variable and 1 equation, so we can solve for X....

(15X)(11) = (7X+12)(15)
(X)(11) = (7X+12)(1)
11X = 7X + 12
4X = 12
X = 3

With this X, we can figure out the initial number of dogs and cats...

Initial dogs = 15X = 15(3) = 45

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Re: In a certain animal shelter, the ratio of the number of dogs to the nu  [#permalink]

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New post 30 Dec 2018, 13:11
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shasadou wrote:
In a certain animal shelter, the ratio of the number of dogs to the number of cats is 15 to 7. If 12 additional cats were to be taken in by the shelter, the ratio of the number of dogs to the number of cats would be 15 to 11. How many dogs are in the shelter?

A. 15
B. 25
C. 30
D. 45
E. 60


Here's a solution that involves 2 variables

In a certain animal shelter, the ratio of the number of dogs to the number of cats is 15 to 7
Let D = number of dogs in shelter
Let C = number of cats in shelter
We can write: D/C = 15/7
Cross multiply to get: 7D = 15C
Rewrite as: 15C - 7D = 0

If 12 additional cats were to be taken in by the shelter, the ratio of the number of dogs to the number of cats would be 15 to 11
So, C + 12 = RESULTING number of cats in the shelter
We can write: D/(C + 12) = 15/11
Cross multiply to get: 11D = 15(C + 12)
Expand right side to get: 11D = 15C + 180
Rewrite as: 12C - 11D = -180

How many dogs are in the shelter?
We have the following system:
15C - 7D = 0
12C - 11D = -180

Subtract the bottom equation from the top equation to get: 4D = 180
Solve: D = 45

Answer: D

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Brent
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Re: In a certain animal shelter, the ratio of the number of dogs to the nu   [#permalink] 30 Dec 2018, 13:11
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