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The ratio of dogs to cats at a certain shelter in City X is 2:3 and

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The ratio of dogs to cats at a certain shelter in City X is 2:3 and  [#permalink]

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New post 01 May 2017, 02:36
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The ratio of dogs to cats at a certain shelter in City X is 2:3 and the ratio of cats to dogs at a different shelter in City Y is 7:3. If there are 300 more cats and dogs at the shelter in City Y than in City X, and the combined ratio of dogs to cats for the two shelters combined is 8:17, how many cats and dogs are at the shelter in City Y?

A. 100
B. 300
C. 350
D. 400
E. 450

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The ratio of dogs to cats at a certain shelter in City X is 2:3 and  [#permalink]

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New post Updated on: 01 May 2017, 07:52
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The ratio of dogs to cats at a certain shelter in City X is 2:3 and the ratio of cats to dogs at a different shelter in City Y is 7:3. If there are 300 more cats and dogs at the shelter in City Y than in City X, and the combined ratio of dogs to cats for the two shelters combined is 8:17, how many cats and dogs are at the shelter in City Y?

At X, dogs: cats = 2:3 or 2x:3x. Total dogs+cats = 2x+3x=5x

At Y, dogs: cats = 3:7 or 3y:7y. Total dogs+cats = 3y+7y=10y

According to 1st condition, 10y-5x=300 ---> 2y-x=60

According to 2nd condition, (2x+3y)/(3x+7y) = 8/17 ---> 34x+51y=24x+56y ---> 2x=y

Solving above 1 eqns, we get x=20 and y=40.

Total cats and dogs at Y = 10y = 400.

Hence, D will be the answer.
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Originally posted by 14101992 on 01 May 2017, 03:45.
Last edited by 14101992 on 01 May 2017, 07:52, edited 1 time in total.
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Re: The ratio of dogs to cats at a certain shelter in City X is 2:3 and  [#permalink]

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New post 01 May 2017, 03:58
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Bunuel wrote:
The ratio of dogs to cats at a certain shelter in City X is 2:3 and the ratio of cats to dogs at a different shelter in City Y is 7:3. If there are 300 more cats and dogs at the shelter in City Y than in City X, and the combined ratio of dogs to cats for the two shelters combined is 8:17, how many cats and dogs are at the shelter in City Y?

A. 100
B. 300
C. 350
D. 400
E. 450


Line to focus at is first ratio is the ratio of Dogs to Cats while second ratio is ratio of Cats to Dogs

In City X
Dog = 2a
Cats = 3a
Total Cats and Dogs = 5a

In City Y
Cat = 7b
Dogs = 3b
Total Cats and Dogs = 10b

Given, 10b = 300 + 5a
i.e. 2b = 60+a

also Cat/Dogs = (3a+7b)/(2a+3b) = 17/8
i.e. 24a + 56b = 34a + 51b
i.e. 5b = 10a
i.e. b = 2a

i.e. 2(2a) = 60+a
i.e. a = 20

i.e. b = 2*20 = 40
Total Animals in Y = 10b = 400

Answer: Option D
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Re: The ratio of dogs to cats at a certain shelter in City X is 2:3 and  [#permalink]

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New post 01 May 2017, 04:53
1
I, Always go by answers for such questions
Condition 1 : There are 300 more cats and dogs at the shelter in City Y
We can strike away A,B

So we start evaluating answer choice C.
If total number of cats & dogs is 350, CityX has 50 and CityY has 350
According to ratios, we will have
CATS:DOGS(City X) 20,30
CATS:DOGS(City Y) 105:245
Adding them doesn't give us our final ratio(8:17)

Next Option D : 400
If total number of cats & dogs is 400, CityX has 100 and CityY has 400
According to ratios, we will have
CATS:DOGS(City X) 40,60
CATS:DOGS(City Y) 120,280
Adding them we get our final ratio(8:17) of cats and dogs. (Option D)
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Re: The ratio of dogs to cats at a certain shelter in City X is 2:3 and  [#permalink]

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New post 06 May 2017, 17:13
Bunuel wrote:
The ratio of dogs to cats at a certain shelter in City X is 2:3 and the ratio of cats to dogs at a different shelter in City Y is 7:3. If there are 300 more cats and dogs at the shelter in City Y than in City X, and the combined ratio of dogs to cats for the two shelters combined is 8:17, how many cats and dogs are at the shelter in City Y?

A. 100
B. 300
C. 350
D. 400
E. 450


We can create the following two ratios:

Ratio of dogs to cats in City X is 2x : 3x

Ratio of cats to dogs in City Y is 7y : 3y, or equivalently, the ratio of dogs to cats in City Y is 3y : 7y

Since there are 300 more cats and dogs at the shelter in City Y than in City X, we can create the following equation:

2x + 3x + 300 = 7y + 3y

5x + 300 = 10y

5x = 10y - 300

x = 2y - 60

Since the combined ratio of dogs to cats for the two shelters combined is 8:17, we can create the following equation:

(2x + 3y)/(3x + 7y) = 8/17

17(2x + 3y) = 8(3x + 7y)

34x + 51y = 24x + 56y

10x = 5y

2x = y

Since y = 2x, we can substitute 2x for y in the equation x = 2y - 60 and we have:

x = 2(2x) - 60

x = 4x - 60

-3x = -60

x = 20

Thus y = 2x = 40, and the number of dogs and cats at the shelter in city Y is 3y + 7y = 10y = 10(40) = 400.

Answer: D
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Re: The ratio of dogs to cats at a certain shelter in City X is 2:3 and  [#permalink]

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New post 15 Apr 2018, 08:00
Let "T" be the Total number of Dogs and Cats in City Shelter X. Therefore Total number of Dogs and Cats in City Shelter Y will be "T+300".

From the information develop this equation:-
(2/5)T + (3/10)(T+300)=(8/25)(2T+300)

Solve for T to get "T=100", i.e. Total number of Dogs and Cats in City Shelter X.
Therefore the Total number of Dogs and Cats in City Shelter Y is "T+300"="100+300"=400 - ANS - "D"

PS: Conceptually the equation mentioned above equates the number of Dogs in City shether X & Y with Today number of Dogs in cobined shelters. Please note that for doing so the equation uses "T", i.e. the total number of dogs and cats. Hence we could get to the answer by developing a linear equation in one variable. I hope this was helpful to everyone.
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Re: The ratio of dogs to cats at a certain shelter in City X is 2:3 and  [#permalink]

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New post 22 Sep 2018, 12:06
The fastest way to solve this problem is by leveraging the weighted average mapping concept. In the City X shelter, dogs represent 40% (2 out of 5 parts) of the total cats and dogs, in the City Y shelter, dogs represent 30% (3 out of 10 parts) of the total cats and dogs, and in the combined shelter, dogs represent 32% (8 out of 25 parts) of the total cats and dogs. Map this out as you would any weighted average problem:

City Y----------Combined----------------------------------------City X
30% -------------- 32% -----------------------------------------40%

This means the ratio of total pets at City Y to City X is 8 :2 or 4:1 This means y = 4x and you know y = x + 300 so x = 100 and y = 400. Correct answer is D.
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Re: The ratio of dogs to cats at a certain shelter in City X is 2:3 and &nbs [#permalink] 22 Sep 2018, 12:06
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