You are given a bag with 100 coins. The bag only has pennies, dimes and half-dollars. The bag has at least one of each coin. The total value of the coins in the bag is worth $5, How many dimes are in the bag?
2026-03-27 07:37:22.1774597042
Count the number of dimes?
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Let $P$ be the number of pennies, $D$ the number of dimes, and $H$ the number of half-dollars.
We have $P+D+H=100$ and $P+10D+50H=500$.
Subtract the former from the latter and we have $9D+49H=400$.
There is only one integer pair solution $(D,H)$ to that last equation, and that solves the problem.