Question

Four years ago, Jane was twice as old as Sam. Four years on from now, Sam will be 3/4 of Jane's age. How old is Jane now?

Answer 1

ok now that i got that out of my system, lets see if we can do it.

Answer 2

LOL @satellite's attachement

Answer 3

Let J denote Jane's current age, and S Sam's current age
(J - 4) = 2(S - 4)
(J + 4) = 3/4 (S + 4)
Solve the system for J.

Answer 4

K thanks

Answer 5

I think I got it wrong... I think the second equation should be 3/4 (J + 4) = (S + 4)

Answer 6

looks good to me. i was trying something that i thought might be simpler but it was more complicated

Answer 7

i will write it anyway, and see if it makes sense

Answer 8

Yep I was definitely wrong in my first post. It should be
J - 4 = 2(s - 4)
3/4 (J + 4) = S + 4
In which case you should get J=12, S=8

Answer 9

as per marine,
\[J-4=2(S-4)\]
\[J-4=2S-8\]
\[J=2S-4\] is one equation. the next one is
\[\frac{3}{4}(J+4)=S+4\]
\[\frac{3}{4}J+3=S+4\]
\[\frac{3}{4}J-1=S\]

now we can substitute
\[J=\frac{3}{4}J-1\] for S in the first equation and get
\[J=2\times \frac{3}{4}(J-1)-4\]
\[J=\frac{3}{2}J-6\]
\[6=\frac{1}{2}J\]
\[J = 12\]