SOLUTION: In five years a boy will be two thirds as old as his uncle. three years ago, he was half as old as his uncle is now. how old are the boy and his uncle now?

Question 802645: In five years a boy will be two thirds as old as his uncle. three years ago, he was half as old as his uncle is now. how old are the boy and his uncle now?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let b = boys present age
let u = uncles present age
:
Write an equation for each statement, simplify as much as possible
"In five years a boy will be two thirds as old as his uncle.
b + 5 = (u+5)
Get rid of the fraction, multiply both sides by 3
3(b + 5) = 2(u + 5)
3b + 15 = 2u + 10
3b = 2u + 10 - 15
3b = 2u - 5
:
" three years ago, he was half as old as his uncle is now."
b - 3 = u
multiply both sides by 2
2(b-3) = u
2b - 6 = u
Using substitution; from the above equation replace u with (2b-6) in the 1st equation
3b = 2(2b - 6) - 5
3b = 4b - 12 - 5
3b = 4b - 17
17 = 4b - 3b
b = 17 yrs is the age of the boy
then
u = 2(17) - 6
u = 28 yrs is the uncle
:
You can see if this checks out in both statements

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