Question 312095
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 = {{{57/3}}}
t = 19 yrs ago