1968 AMC 12 Problem 19
Attempt Problem 19 of the 1968 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 1968 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
Let be the number of ways that dollars can be changed into dimes and quarters, with at least one of each coin being used. Then equals:
Answer: E
Small hint:
In cents, solve
Big hint:
Use parity to write , then enforce positive coin counts
Solution:
The equation reduces to Thus must be even; write giving Positivity requires so there are ways.
Therefore, the correct answer is E.
Problem 19 in other years
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