Let
J = present age of Jane
S = present age of Sam
see table below,
[tex]\begin{bmatrix}&Name &Past &Present &Future\\&Jane &J-4 &J &J+4\\&Sam &S-4 &S &S+4\end{bmatrix}[/tex]
Conditions:
#1. Four years ago, Jane was twice as old as Sam
so we can say that 4 years ago J = 2S.
Now refer to table above. To get the correct equation, we should also consider their age 4 years ago. So the correct equation is now,
J - 4 = 2(S - 4)
#2. Four years on from now, Sam will be 3/4 of Jane's
so we can say that 4 years from now, S = ¾J
Now refer to table above again. To get the correct equation, we should also consider their age 4 years from now. So the correct equation is now,
S + 4 = ¾(J + 4)
Now we have 2 unknowns and 2 equations. So we can solve the missing variables.
J - 4 = 2(S - 4)
J - 4 = 2S - 8
J = 2S - 8 + 4
J = 2S - 4
substitute J in the 2nd equation,
S + 4 = ¾(J + 4)
S + 4 = ¾(J + 4)
S + 4 = ¾(2S - 4 + 4)
S + 4 = 6S/4
S + 4 = 3S/2
2S + 8 = 3S
S = 8
J = 2S - 4
J = 2(8) - 4
J = 16 - 4
J = 12
So the present age of Jane is 12 years old and present age of Sam is 8 years old.
