1953 AMC 12 Problem 1

Attempt Problem 1 of the 1953 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 1953 AMC 12 solutions, or check the answer key.

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

A boy buys oranges at

3

for

10

cents. He will sell them at

5

for

20

cents. In order to make a profit of

\$1.00,

he must sell:

67

oranges

150

oranges

200

oranges

an infinite number of oranges

none of these

Find the buying cost and selling price per orange

The profit per orange is the difference of the two unit rates

Each orange costs

\frac{10}{3}

cents and sells for

4

cents, so the profit is

4-\frac{10}{3}=\frac{2}{3}

cent per orange. To earn

100

cents, he must sell

\frac{100}{\frac{2}{3}}=150

oranges.

Thus, the correct answer is B.

Problem 1 in other years