2002 AMC 8 Problems/Problem 2

Problem

How many different combinartions of <dollar></dollar>5 bills and <dollar></dollar>2 bills can be used to make a total of <dollar></dollar>17? Order does not matter in this problem.

$\text {(A)}\ 2 \qquad \text {(B)}\ 3 \qquad \text {(C)}\ 4 \qquad \text {(D)}\ 5 \qquad \text {(E)}\ 6$

Solution

You cannot use more than $4$ <dollar></dollar>5 bills, but if you use $3$ <dollar></dollar>5 bills, you can add another <dollar></dollar>2 bill to make a combination. You can also use $1$ <dollar></dollar>5 bill and $6$ <dollar></dollar>2 bills to make another combination. There are no other possibilities, as making <dollar></dollar>17 with $0$ <dollar></dollar>5 bills is impossible, so the answer is $\boxed {\text {(A)}\ 2}$ .

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2002 AMC 8 Problems/Problem 2

Problem

Solution