2010 AMC 8 Problems/Problem 7

Problem

Using only pennies, nickels, dimes, and quarters, what is the smallest number of coins Freddie would need so he could pay any amount of money less than a dollar?

$\textbf{(A)}\ 6 \qquad\textbf{(B)}\ 10\qquad\textbf{(C)}\ 15\qquad\textbf{(D)}\ 25\qquad\textbf{(E)}\ 99$

Solution

If he has $3$ quarters, his other coins are able to pay amount amount less than or equal to $25$ cents, because it can just be added on to the value of his quarters. If he has $2$ dimes and $1$ nickel, he can pay any amount that is a multiple of $5$ . Lastly, Freddie need $4$ pennies for a total of $3+2+1+4=\boxed{\textbf{(B)}\ 10}$ coins.

2010 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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2010 AMC 8 Problems/Problem 7

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