SOLUTION: Akosua is A years now. Abigail is B years older than Akosua. In ( X + 2 ) years time, AKosua will be half as old as Abigail. Find X

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Question 985208: Akosua is A years now. Abigail is B years older than Akosua. In ( X + 2 ) years time, AKosua will be half as old as Abigail. Find X
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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let ak = Akosua's age
let ab = Abigail's age
:
Akosua is A years now.
ak = A
:
Abigail is B years older than Akosua.
ab = ak + B

In (X + 2) years time, AKosua will be half as old as Abigail.
ak + (x+2) = 1%2F2(ab+ (x+ 2))
multiply both sides by 2
2(ak + x + 2) = ab + x + 2
2ak + 2x + 4 = ab + x + 2
2ak + 2x - x = ab + 2 - 4
2ak + x = ab - 2
replace ab with (ak+B)
2ak + x = ak + B - 2
x = ak - 2ak + B - 2
x = -ak + B - 2
Replace Ak with A
x = -A + B - 2