1959 AMC 12 Problem 9

Attempt Problem 9 of the 1959 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 1959 AMC 12 solutions, or check the answer key.

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

A farmer divides his herd of

n

cows among his four sons so that one son gets one-half the herd, a second son one-fourth, a third son one-fifth, and the fourth son

7

cows. Then

n

is:

80

100

140

180

240

Add the three fractional shares of the herd

The fraction left over corresponds to

7

cows

The first three sons receive

\frac12+\frac14+\frac15=\frac{19}{20}

of the herd. Thus the remaining

\frac{1}{20}

of the herd is

7,

n=140.

Therefore, the correct answer is C.

Problem 9 in other years