Problem:
A softball team played ten games, scoring , and 10 runs. They lost by one run in exactly five games. In each of their other games, they scored twice as many runs as their opponent. How many total runs did their opponents score?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The softball team could only have scored twice as many runs as their opponent when they scored an even number of runs. In those games their opponents scored
In the games the softball team lost, their opponents scored
The total number of runs scored by their opponents was runs.
The problems on this page are the property of the MAA's American Mathematics Competitions