SOLUTION: The sum of 6 consecutive odd numbers is 132. What is the sum of all the tens digits of these numbers?

Question 1012016: The sum of 6 consecutive odd numbers is 132. What is the sum of all the tens digits of these numbers?
Found 2 solutions by ikleyn, KMST:
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.
Let x be the smallest of these numbers.

Then the numbers are x, x+2, x+4, x+6, x+8 and x+10.

Their sum is 6x + 30.

Hence,

6x + 30 = 132,
6x = 132-30 = 102.
x = = 17.

The numbers are 17, 19, 21, 23, 25, 27.

The rest is on you.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Six consecutive odd numbers (or six consecutive even numbers)
could be represented by
, , , , , and .
The sum would be

In this case,
-->-->-->--> .
So the numbers are 17, 19, 21, 23, 25, and 27.
The sum of all the tens digits is
.

Another way:
If the sum is , the average is .
Consecutive odd integers form an arithmetic sequence,
and in an arithmetic sequence, the average (or mean) is also the median.
That means that of the 6 consecutive odd numbers are more than , with a for a tens digit,
and the other are less than , including and .
So of the six odd numbers have a as a tens digit, and the other have a as the tens digit.
So the sum of the tens digits is
.

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