Question 840089
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.