1953 AMC 12 Problem 6

Attempt Problem 6 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).

6.

Charles has 5q+15q+1 quarters and Richard has q+5q+5 quarters. The difference in their money in dimes is:
10(q−1)10(q-1)
25(4q−4)\dfrac25(4q-4)
25(q−1)\dfrac25(q-1)
52(q−1)\dfrac52(q-1)
none of these
Answer: A
Concepts:currency conversionalgebraic expression
Small hint:
First subtract the two numbers of quarters
Big hint:
One quarter is 52\frac{5}{2} dimes
Solution:
The difference is (5q+1)−(q+5)=4q−4 (5q+1)-(q+5)=4q-4 quarters. Multiplying by 52\frac{5}{2} dimes per quarter gives 52(4q−4)=10(q−1). \frac52(4q-4)=10(q-1).
Thus, the correct answer is A.
LIVE by Po-Shen Loh
Programs

LIVE Classes

Self-Paced Classes

Stars

Scholarship

About Us

Who Is Po-Shen Loh?

Email Contact

Newsletter

Jobs

Become a Star

For a more Thought Full world.

© 2026 Expii, Inc.