Question

Three yrs ago Reagan was three times as old as Sarah and half as old as Lauren. Three yrs from now, Reagan will be twice as old as Sarah.  How old are they now?

Answer 1

Reagan (R)
Sara (S)
Lauren (L)

R-3 (Reagan's age 3 years ago...)
we have 3 equations with 3 variables:

R-3 = 3 * (S-3) -> R -3 = 3S - 9 -> R = 3S -6
R-3 = (L-3) / 2 -> 2R -6 = L - 3 -> L = 2R -3
R+3 = 2 * (S+3) -> R +3 = 2S + 6 -> R = 2S +3

3S - 6 = 2S + 3 -> S = 9
R = 2 * 9 +3 = 21
L = 2 * 21 -3 = 39

Reagan is 21
Sara is 9
Lauren is 39

3 years ago - Reagan was 18 - 3 X Sara who was 6
3 years from now - Reagan will be 24 - 2 X Sara who will be 12