1964 AMC 12 Problem 14

Attempt Problem 14 of the 1964 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 1964 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

14.

A farmer bought

749

sheep. He sold

700

of them for the price paid for the

749

sheep. The remaining

49

sheep were sold at the same price per head as the other

700.

Based on the cost, the percent gain on the entire transaction is:

6.5

6.75

7

7.5

8

Let the total purchase cost be

C

The selling price per sheep is

\frac{C}{700}

Let the total cost be

C.

Since the first

700

sheep sell for

C,

each sheep sells for

\frac{C}{700}.

Total revenue is therefore

\frac{749C}{700}=1.07C,

7\%

gain.

Thus, the correct answer is C.

Problem 14 in other years