SOLUTION: The average of 5 consecutive odd integers is 6 less than the sum of the largest two. What is the smallest?

Question 1093117: The average of 5 consecutive odd integers is 6 less than the sum of the largest two. What is the smallest?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

There is no solution to the problem.

Since we are talking about the average of 5 consecutive odd numbers, let's choose x to be the middle number, since it is the average. Then the numbers are x-4, x-2, x, x+2, and x+4. The problem says the average is 6 less than the sum of the largest two. That gives us

which gives us the answer x=0, making the 5 numbers -4, -2, 0, 2, and 4.

But the problem requires the five numbers to be consecutive odd integers -- so there is no solution.
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