The smallest of the three consecutive odd integers

Question

Find three consecutive odd integers such that the sum of the first, two times the second, and three times the third is 34.

Answer 1

Consecutive odd integers are two apart, for example: 7, 9 , 11.

Let x = 1st odd integer. Then the next two can be represented by x + 2 and x + 4.

x + 2(x+2) + 3(x+4) = 34

x + 2x + 4 + 3x + 12 = 34

6x + 16 =34

6x = 18

x = 3 (if this was not odd, then the problem would have no solution)

x+2 = 5

x+4= 7

Check:

1st is 3.

2 times the 2nd: 10

3 times the 3rd: 21

3 + 10 + 21 = 34