2021 JMPSC Problems/Problem 2

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 $11+3=14$.