Question
The ratio of the number of hens to the number of goats
on farm A is 5:4 and that on farm B is 5:7. What could be ratio of the total number of hens to the total number of goats in farms A and B taken together?Solution
Given Ratios: Farm A: Hens to goats = 5:4 Farm B: Hens to goats = 5:7 Assume numbers based on ratios: Farm A: 5x hens and 4x goats Farm B: 5y hens and 7y goats Total hens and goats: Total hens = 5x + 5y Total goats = 4x + 7y Combined Ratio: Ratio of hens to goats= (5x+5y/4x+5y) Simplify by choosing x and y: Let x=7 and y=4: Hens on A = 5(7) = 35 Goats on A = 4(7) = 28 Hens on B = 5(4) = 20 Goats on B = 7(4) = 28 Calculate totals: Total hens = 35 + 20 = 55 Total goats = 28 + 28 = 56 Final Ratio: = (55/56)
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