SOLUTION: The sum of three integers is 169. The first integer is twelve more than the second integer. The third integer is fifteen less than the sum of the first and second integers. What ar

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Question 1152479: The sum of three integers is 169. The first integer is twelve more than the second integer. The third integer is fifteen less than the sum of the first and second integers. What are the integers?
Answer by ikleyn(52858) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x = the second integer.

Then the first integer is (x+12),  and the third integer is (x + (x+12) - 15) = (2x-3).


The equation for the total is 


    x + (x+12) + (2x-3) = 169.


Simplify and solve


    4x + 9 = 169

    4x = 169 - 9 = 160

     x = 160/4 = 40.


ANSWER.  2nd number is 40;  1st number is 40+12 = 52;  3rd number is 40+52-15 = 77.


CHECK.  40 + 52 + 77 = 169.   ! Correct !

Solved.