1955 AMC 12 Problem 6

Attempt Problem 6 of the 1955 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 1955 AMC 12 solutions, or check the answer key.

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

A merchant buys a number of oranges at

3

for

10

¢ and an equal number at

5

for

20

¢. To “break even” he must sell all at:

8

for

30

3

for

11

5

for

18

11

for

40

13

for

50

Use

15

oranges in each equal-sized purchase so that both quoted rates divide evenly

Compare the total cost of

30

oranges with each proposed selling rate

Suppose he buys

15

oranges at each rate. The first

15

cost

50

¢ and the second

15

cost

60

¢, for

110

¢ total. Thus

30

oranges must sell for

110

¢, which is equivalent to

3

for

11

¢.

Therefore, the correct answer is B.

Problem 6 in other years