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Rate problem with x cows

Source: 1976 AHSME Problem 13

May 17, 2014
AMC

Problem Statement

If xx cows give x+1x+1 cans of milk in x+2x+2 days, how many days will it take x+3x+3 cows to give x+5x+5 cans of milk?
<spanclass=′latex−bold′>(A)</span>x(x+2)(x+5)(x+1)(x+3)<spanclass=′latex−bold′>(B)</span>x(x+1)(x+5)(x+2)(x+3)<span class='latex-bold'>(A) </span>\frac{x(x+2)(x+5)}{(x+1)(x+3)}\qquad<span class='latex-bold'>(B) </span>\frac{x(x+1)(x+5)}{(x+2)(x+3)}\qquad
<spanclass=′latex−bold′>(C)</span>(x+1)(x+3)(x+5)x(x+2)<spanclass=′latex−bold′>(D)</span>(x+1)(x+3)x(x+2)(x+5)<spanclass=′latex−bold′>(E)</span>none of these<span class='latex-bold'>(C) </span>\frac{(x+1)(x+3)(x+5)}{x(x+2)}\qquad<span class='latex-bold'>(D) </span>\frac{(x+1)(x+3)}{x(x+2)(x+5)}\qquad <span class='latex-bold'>(E) </span>\text{none of these}
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