Difference between revisions of "2002 AMC 8 Problems/Problem 2"

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==Problem==
 
==Problem==
  
How many different combinations of <dollar>5</dollar> bills and <dollar>2</dollar> bills can be used to make a total of <dollar>17</dollar>? Order does not matter in this problem.
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How many different combinations of \$5 bills and \$2 bills can be used to make a total of \$17? Order does not matter in this problem.
  
 
<math>\text {(A)}\ 2 \qquad \text {(B)}\ 3 \qquad \text {(C)}\ 4 \qquad \text {(D)}\ 5 \qquad \text {(E)}\ 6</math>
 
<math>\text {(A)}\ 2 \qquad \text {(B)}\ 3 \qquad \text {(C)}\ 4 \qquad \text {(D)}\ 5 \qquad \text {(E)}\ 6</math>

Revision as of 11:19, 14 June 2016

Problem

How many different combinations of $5 bills and $2 bills can be used to make a total of $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 $\boxed {\text {(A)}\ 2}$.

See Also

2002 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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