Verified answer

Let Sam's age be x years

Ray = x+15 years

Bert = x +12 years

ADD 3x +27 = 42

3x = 15

x = 5

ANSWER Sam = 5 years Ray = 20 years Bert = 17 years

CHECK

5+20+17 = 42 years

r: age of Ray

s: age of Sam

b: age of Bert

r = 15 + s: Ray is 15 years older than Sam

s = b - 12: Sam is 12 years younger than Bert

r + s + b = 42: Their ages total 42

This is a system of 3 linear equations. I don't think systematic ways of solving are the way to go here. Instead, notice that we can eliminate r from the last equation by subbing in: r = 15 + s:

r + s + b = (15 + s) + s + b = 42

Now, we can eliminate b by subbing in from the second equation:

s = b - 12 --> b = s + 12

--> plug in to summation

(15 + s) + s + (s + 12) = 42

--> simplify

3s + 27 = 42

--> subtract 27

3s = 15 --> s = 15/3 = 5

Now, b = s + 12 = 5 + 12 = 17

r = 15 + s = 15 + 5 = 20

So Sam is 5 years old, Bert is 17, and Ray is 20.

Ray = x

x-15 = Sam

x-3 = Bert

x + x - 15 + x - 3 = 42

3x - 18 = 42

3x = 60

x=20

Ray = 20

Sam = 20-15 = 5

Bert = 20-3=17

20, 5, 17

Ray is 20

Sam is 5

Bert is 17

Okay i did this in my head so bert is 17 sam is 5 and ray is 20. It seems correct to me but in tired and i did it in my head so you should double check