Art of Problem Solving

2021 JMPSC Problems/Problem 2

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Problem

Brady has an unlimited supply of quarters ($\$0.25$), dimes ($\$0.10$), nickels ($\$0.05$), and pennies ($\$0.01$). What is the least number (quantity, not type) of coins Brady can use to pay off $\$2.78$?

Solution

To minimize the number of coins, we need to maximize the amount of high-valued coins we use. 11 quarters are worth $\$2.75$, which is the most quarters we can use to get a value less than or equal to $\$2.78$. Finally, we can add 3 pennies to get a total of $\$2.87$, so the answer is $11+3=14$.