Find three consecutive odd integers such that three times the difference of the third and first odd integer is five less than the second odd integer

Question

I’m having a hard time trying to figure this out. I’ve tried using X+2( second integer) and x+3 as well and just barely miss the mark for the answer.

Answer 1

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.