1954 AMC 12 Problem 23

Attempt Problem 23 of the 1954 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 1954 AMC 12 solutions, or check the answer key.

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

23.

If the margin made on an article costing

C

dollars and selling for

S

dollars is

M=\dfrac1nC,

then the margin is given by:

M=\dfrac1{n-1}S

M=\dfrac1nS

M=\dfrac n{n+1}S

M=\dfrac1{n+1}S

M=\dfrac n{n-1}S

Use

S=C+M

together with

M=\frac{C}{n}

Express

C

in terms of

S

, then divide by

n

Since

S=C+M=C+\frac{C}{n},

\begin{aligned} S&=\frac{n+1}{n}C,\\ C&=\frac n{n+1}S. \end{aligned}

Therefore

M=\frac Cn=\frac1{n+1}S.

Thus, the correct answer is D.

Problem 23 in other years