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

3, 5, 7

Step-by-step explanation:

If x is the smallest number, then the other two numbers are x+2 and x+4.

The sum of the first, two times the second, and three times the third, is 34.

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

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

6x + 16 = 34

x = 3

So the numbers are 3, 5, and 7.