Question

Ava has some dimes and some quarters. She has no less than 15 coins worth no more than $2.25 combined. If Ava has 2 quarters, determine the maximum number of dimes that she could have. If there are no possible solutions, submit an empty answer.

Answer 1

17 dimes

Explanation:

The given relations can be satisfied by 12 combinations of coins, but the question only asks about one of them: the maximum number of dimes when there are 2 quarters.

When there are 2 quarters, the problem reduces to finding the maximum number of dimes such that the number is at least 15 -2 = 13 and has a value at most $2.25 - 2×$0.25 = $1.75.

The number of dimes cannot be $1.75/$0.10 = 17.5, but it can be 17. That number is more than 13, so ...

the maximum number of dimes Ava could have is 17.