Jeff is 6 years older than Sam. In 4 years, he will be twice as old as Sam was 5 years ago. Find their ages now.

Answer 1

J=6+S

J+4 = 2(S-5)

6+S+4 = 2S-10

S = 20

J=26

Answer 2

MJ,

Set it up in algebraic equations. If Jeff is 6 years older than Sam, write this as J = S + 6.

In 4 years, Jeff will be twice as old as Sam was 5 years ago; write that as J + 4 = 2(S - 5).

Rewrite second equation after distributing the 2, so that we have J + 4 = 2S - 10.

Rewrite your second equation after subtracting 4 from each side, so that you have J = 2s - 14.

Set our first and second equations equal to each other since obviously Jeff's age is equal to Jeff's age.

2s - 14 = s + 6.

Add 14 to each side to get 2s = s + 20. Subtract s from each side to get s = 20.

Now we know that Sam is 20 years old, and therefore that Jeff is 26.

Plug the numbers back into both original equations to check our work.

Hope this helps! :)