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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Scott Woodbury-Stewart

Founder and CEO

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