1976 AMC 12 Problem 13

Attempt Problem 13 of the 1976 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1976 AMC 12 solutions, or check the answer key.

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13.

x

cows give

x+1

cans of milk in

x+2

days, how many days will it take

x+3

cows to give

x+5

cans of milk?

\frac{x(x+2)(x+5)}{(x+1)(x+3)}

\frac{x(x+1)(x+5)}{(x+2)(x+3)}

\frac{(x+1)(x+3)(x+5)}{x(x+2)}

\frac{(x+1)(x+3)}{x(x+2)(x+5)}

none of these

First find the number of cans produced per cow-day

Set

\frac{x+5}{(x+3)T}=\frac{x+1}{x(x+2)}

The production rate is

\frac{x+1}{x(x+2)}

cans per cow-day. If the new time is

T,

then

\frac{x+5}{(x+3)T}=\frac{x+1}{x(x+2)}.

Hence

T=\frac{x(x+2)(x+5)}{(x+1)(x+3)}.

Therefore, the correct answer is A.

Problem 13 in other years