document.write( "Question 1012016: The sum of 6 consecutive odd numbers is 132. What is the sum of all the tens digits of these numbers? \n" ); document.write( "

Algebra.Com's Answer #627851 by KMST(5328) $\"\"$ $\"About$

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Six consecutive odd numbers (or six consecutive even numbers)
\n" ); document.write( "could be represented by
\n" ); document.write( " $\"n\"$ , $\"n%2B2\"$ , $\"n%2B4\"$ , $\"n%2B6\"$ , $\"n%2B8\"$ , and $\"n%2B10\"$ .
\n" ); document.write( "The sum would be
\n" ); document.write( "

\n" ); document.write( "In this case,
\n" ); document.write( " $\"6n%2B30=132\"$ --> $\"6n=132-30\"$ --> $\"6n=102\"$ --> $\"n=102%2F6\"$ --> $\"n=17\"$ .
\n" ); document.write( "So the numbers are 17, 19, 21, 23, 25, and 27.
\n" ); document.write( "The sum of all the tens digits is
\n" ); document.write( " $\"1%2B1%2B2%2B2%2B2%2B2=10\"$ .
\n" ); document.write( "
\n" ); document.write( "Another way:
\n" ); document.write( "If the sum is $\"132\"$ , the average is $\"132%2F6=22\"$ .
\n" ); document.write( "Consecutive odd integers form an arithmetic sequence,
\n" ); document.write( "and in an arithmetic sequence, the average (or mean) is also the median.
\n" ); document.write( "That means that $\"6%2F2=3\"$ of the 6 consecutive odd numbers are more than $\"22\"$ , with a $\"2\"$ for a tens digit,
\n" ); document.write( "and the other $\"3\"$ are less than $\"22\"$ , including $\"21\"$ $\"19\"$ and $\"17\"$ .
\n" ); document.write( "So $\"4\"$ of the six odd numbers have a $\"2\"$ as a tens digit, and the other $\"2\"$ have a $\"1\"$ as the tens digit.
\n" ); document.write( "So the sum of the tens digits is
\n" ); document.write( " $\"4%2A2%2B2%2A1=8%2B2=10\"$ .
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