1987 AHSME Problems/Problem 17
Problem
In a mathematics competition, the sum of the scores of Bill and Dick equalled the sum of the scores of Ann and Carol. If the scores of Bill and Carol had been interchanged, then the sum of the scores of Ann and Carol would have exceeded the sum of the scores of the other two. Also, Dick's score exceeded the sum of the scores of Bill and Carol. Determine the order in which the four contestants finished, from highest to lowest. Assume all scores were nonnegative.
Solution
Let the scores be , , , and . Then we have , , and . Call these equations , , and respectively. Then adding and gives . Now subtracting from gives . Finally from , since and is non-negative, we must have , so putting our results together we get , which is answer .
See also
1987 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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