Average problem 1 by Dhaval Furia
The average of integers is . Among these integers, there are exactly which do not exceed . What is the highest possible value of the average of these integers?
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1 solution
In order to maximize the average of the 20 integers, we need to maximize their sum, which can be done by minimizing the sum of the other 10 (out of 30) integers which do exceed 5
That is possible when those 10 are 6 each, making their average 6
Now a simple application of alligation reveals that the average of the first 20 integers is 4.5