1998 CEMC Gauss (Grade 7) Problems/Problem 19

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Problem

Juan and Mary play a two-person game in which the winner gains 2 points and the loser loses 1 point. If Juan won exactly 3 games and Mary had a final score of 5 points, how many games did they play?

$\text{(A)}\ 7 \qquad \text{(B)}\ 8 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 11$

Solution

If Juan won 3 games, then Mary lost 3 points. Mary must have had $3 + 5 = 8$ points at the start, meaning she won 4 games. This makes a total of $3 + 4 = \boxed{7}$ games.

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