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Printjmc
prealgebra intermediate
Problem
Ed takes five 100-point tests in his algebra class. He scores 87, 85 and 87 points on the first three tests. If the scores of his last two tests differ by three points and he has a average on his five tests, what was his highest test score?
Solution
Instead of adding up scores and figuring out the new averages, a quicker way (useful for the countdown round) is as follows:
Since the average is 90, we first calculate how many points below 90 he already is: he's scored 87, 85, and 87, meaning that he is 3, 5, and 3 points below 90 respectively, making for a total of 11 points below. We then know that his remaining two tests must be a combined 11 points above 90, and since they differ by 3 points, we know that one test is 4 above 90, and the other is 7 above 90, meaning his highest score was .
Since the average is 90, we first calculate how many points below 90 he already is: he's scored 87, 85, and 87, meaning that he is 3, 5, and 3 points below 90 respectively, making for a total of 11 points below. We then know that his remaining two tests must be a combined 11 points above 90, and since they differ by 3 points, we know that one test is 4 above 90, and the other is 7 above 90, meaning his highest score was .
Final answer
97