Question 794949: Gabriel, Christian and Sebastian are friends whose ages add up to 26. Five years ago, Christian's age is twice that of Gabriel's. Seven years from now, Sebastian's age will be thirteen less than the sum of the ages of Gabriel and Christian. How old is Christian?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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
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