Question 802645
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 = {{{2/3}}}(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 = {{{1/2}}}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