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.

Let the "three consecutive odd integers" be x, (x+2), and (x+4).

"three times the difference of the third and first odd integer"     means 3*( (x+4) - x )

"is"    means equals

"five less than the second odd integer"      means     (x+2) - 5

     3((x+4)-x) = (x+2) - 5

        12 = x-3

        15 = x

The three odd integers are 15, 17, 19.

Check:

    Is 3(19-15) = 17-5   ?

          3*4 = 12   ?

           12 = 12   ?yes

Now, you may quickly realize that "three times the difference of the third and first odd integer" is 3*4=12, so "five less than the second odd integer" means that it is 12+5=17.  Thus, the three odd integers are 15, 17, 19.

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the solution is 12x-6y