SOLUTION: In 5 years, Tom will be twice as old as Cindy. 13 years ago, he was three times as old as Cindy. How many years ago was Tom four times as old as Cindy?

Question 840089: In 5 years, Tom will be twice as old as Cindy. 13 years ago, he was three times as old as Cindy. How many years ago was Tom four times as old as Cindy?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let t = Tom's present age
let c = Cindy's age
:
Write an equation for each statement. simplify as much as possible
:
In 5 years, Tom will be twice as old as Cindy.
t + 5 = 2(c+5)
t + 5 = 2c + 10
t = 2c + 10 - 5
t = 2c + 5
:
13 years ago, he was three times as old as Cindy.
t - 13 = 3(c-13)
t - 13 = 3c - 39
t = 3c - 39 + 13
t = 3c - 26
Find their present ages, in the 1st equation replace t with (3c-26)
3c - 26 = 2c + 5
3c - 2c = 5 + 26
c = 31 yrs is Cindy's present age
and
t = 2(31) + 5
t = 67 yrs is Tom's
:
How many years ago was Tom four times as old as Cindy?
let y = no. of years for this to be true
67 - y = 4(31-y)
67 - y = 124 - 4y
-y + 4y = 124 - 67
3y = 57
y = 57/3
y = 19 yrs ago
:
I'll let you check this out in the last statement.

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