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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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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
[Reveal] Spoiler: OA

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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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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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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
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
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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] 06 May 2017, 17:13
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