SOLUTION: In five years, Sylvia will be twice as old as Luke. Thirteen years ago, Sylvia was three times as old as Luke. How many years ago was Sylvia four times as old as Luke?

Question 312095: In five years, Sylvia will be twice as old as Luke. Thirteen years ago, Sylvia was three times as old as Luke. How many years ago was Sylvia four times as old as Luke?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
In five years, Sylvia will be twice as old as Luke.
S + 5 = 2(L + 5)
S + 5 = 2L + 10
S = 2L + 10 - 5
S = 2L + 5
;
Thirteen years ago, Sylvia was three times as old as Luke.
S - 13 = 3(L - 13)
S - 13 = 3L - 39
S = 3L - 39 + 13
S = 3L - 26
:
Find L's age
3L - 26 = 2L + 5
3L - 2L = 5 + 26
L = 31 yrs
Find S
S = 2(31) + 5
S = 67 yrs
:
How many years ago was Sylvia four times as old as Luke?
Let t = no. of years for this to be true
S - t = 4(L - t)
67 - t = 4(31 - t)
67 - t = 124 - 4t
4t - t = 124 - 67
3t = 57
t =
t = 19 yrs ago

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