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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.