document.write( "Question 1093117: The average of 5 consecutive odd integers is 6 less than the sum of the largest two. What is the smallest? \n" ); document.write( "

Algebra.Com's Answer #707715 by greenestamps(13200) $\"\"$ $\"About$

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There is no solution to the problem.

\n" ); document.write( "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
\n" ); document.write( " $\"x+=+%28x%2B2%29%2B%28x%2B4%29-6\"$
\n" ); document.write( " $\"x+=+2x%2B6-6\"$
\n" ); document.write( " $\"x+=+2x\"$
\n" ); document.write( "which gives us the answer x=0, making the 5 numbers -4, -2, 0, 2, and 4.

\n" ); document.write( "But the problem requires the five numbers to be consecutive odd integers -- so there is no solution. \n" ); document.write( "

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