SOLUTION: for five consecutive integers, the sum of the even integers is 60. what is the value of the smallest odd integer?

Question 665182: for five consecutive integers, the sum of the even integers is 60. what is the value of the smallest odd integer?
Answer by kevwill(135) (Show Source): You can put this solution on YOUR website!
There are two possibilities to consider here:
1) The five consecutive integers are comprised of 3 odd integers and 2 even integers, or
2) The five consecutive integers are comprised of 3 even integers and 2 odd integers.

For the first case, call the five consecutive integers, x, x+1, x+2, x+3, and x+4. Then the even integers are x+1 and x+3, so we have:
x+1 + x+3 = 60
2x + 4 = 60
2x = 56
x = 28
Which would make the two even integers 29 and 31. However, since these are not odd integers, then there is no solution for the first case.

For the second case, again call the five consecutive integers, x, x+1, x+2, x+3, and x+4. Then the even integers are x, x+2, and x+4, so we have:
x + x+2 + x+4 = 60
3x + 6 = 60
3x = 54
x = 18
Which makes the three even integers 18, 20, and 22. The odd integers are x+1 and x+3, so

The value of the smallest odd integer is 19.

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