SOLUTION: Alan is 12 years older than tom. Three years ago, Tom was half of how old Alan is now. What are there ages now.

Question 1067838: Alan is 12 years older than tom. Three years ago, Tom was half of how old Alan is now. What are there ages now.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let a = Alan's present age
let t = Tom's
:
Write an equation for each statement
:
Alan is 12 years older than tom.
a = t + 12
Three years ago, Tom was half of how old Alan is now.
t - 3 = .5a
t = .5a + 3
:
What are their ages now.
replace a with (t+12) from the first statement
t = .5(t+12) + 3
t = .5t + 6 + 3
t - .5t = 9
.5t = 9
t = 9/.5
t = 18 yrs is Tom's age
therefore
a = 18 + 12
a = 30 yrs is Alan's age
:
:
:
Check this in the statement:
"Three years ago, Tom was half of how old Alan is now."
18 - 3 = .5(30)
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