Question 794949
Gabriel, Christian and Sebastian are friends whose ages add up to 26.
g + c + s = 26
 Five years ago, Christian's age is twice that of Gabriel's.
c -5 = 2(g-5)
c-5 = 2g - 10
c = 2g - 10 + 5
c = 5g - 5
-2g + c = -5
 Seven years from now, Sebastian's age will be thirteen less than the sum of the ages of Gabriel and Christian.
s + 7 = (c+7) + (g+7) - 13
s + 7 = c + g + 14 - 13
s = c + g + 1 - 7 
s - c - g = -6
:
Arrange like the 1st equation and use elimination
-g - c + s = -6
 g + c + s = 26
-----------------adding eliminates g and c, find s
2s = 20
s = 10 yrs is S's age
:
Using the 1st equation, and the rearanged 2nd equation:w
 g + c = 16
-2g +c = -5
-----------------Subtraction eliminates c, find g
3g = 21
g = 7 yrs is G's age
:
How old is Christian?
g + c + s = 26
7 + c + 10 = 26
c = 26 - 17
c = 9 yrs is C's age