# SOLUTION: A famer is trying to decide what to do with his livestock on his farm. He is thinking that he should sell 75 of his ducks, and this would give him enough food to feed the remaining

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 Question 83371: A famer is trying to decide what to do with his livestock on his farm. He is thinking that he should sell 75 of his ducks, and this would give him enough food to feed the remaining ducks for 20 more days than what he currently has. His friend suggests that he buys 100 more ducks, however this will mean that the food he has for the ducks will last 15 days less than it does now. How many ducks does he have and how many days does the food last?Answer by stanbon(60771)   (Show Source): You can put this solution on YOUR website!A famer is trying to decide what to do with his livestock on his farm. ------------- He is thinking that he should sell 75 of his ducks, and this would give him enough food to feed the remaining ducks for 20 more days than what he currently has. Let x be the number of ducks;Let y = number of days they can be fed. Then amount of feed is xy ------------------- Change #1: 75 fewer ducks and 20 additional days. Then amount of feed is (x-75)(y+20) ---------------- His friend suggests that he buys 100 more ducks, however this will mean that the food he has for the ducks will last 15 days less than it does now. Change #2: 100 additional ducks; and 15 fewer days Then amount of feed is (x+100)(y-15) --------- EQUATIONS: The amount of feed has not changed so you get: (x-75)(y+20) = xy 20x-75y=1500 ------------------- (x+100)(y-15) = xy -15x+100y=1500 ----------------- solve for x and y: x = 300 (# of ducks) y = 60 (# of days) ====================== Cheers, Stan H.