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Answer

This is a Before After question.

     Before Transfer After
Farm X  9u  -35  9u – 35
Farm Y 4u  +35  4u + 35 
       

9u – 35 = 4u + 35

9u – 4u = 35 + 35

5u = 70

1u = 70 ÷ 5 = 14

4u = 4 x 14 = 56

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Let the original number of goats in Farm X be x.

Let the original number of goats in Farm Y be y.

Let the final number of goats in Farm X and Y be z

x/y = 9/4

4x = 9y

x – 35 = z

y+35 = z

4(x-35) = 4z

4x – 140 = 4z

9y – 140 = 4z

4(y+35) = 4z

4y + 140 = 4z

9y  – 4y – 140 – 140 = 0

5y – 280 = 0

5y = 280

y =  56

Test for correct answer

56 + 35 + 35 = 126

126/56 = 9/4

Therefore, the answer is proven to be correct.

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