How old will jack be in $5$ years

Question

The question is

Jack is now $14$ years older than Bill. If in $10$ years Jack will be twice as old as Bill, how old will Jack be in $5$ years? (Ans = $23$)

Here is how I am solving it could anyone tell me where I might be going wrong ? \begin{equation} J = 14 + B \tag{i}\label{i} \end{equation} and \begin{equation} J+10 = 2B \tag{ii}\label{ii} \end{equation}

So by inserting \eqref{i} in \eqref{ii} we get$$24=B,$$so Jack is $38$, and after $5$ years he will be $38+5=43$ years old.

Answer 1

In your second equation, you are ten years in the future. With $J$ and $B$ representing Jack and Bill's present age respectively, Bill's age ten years from now is $B+10$ and Jack's age ten years from now is $J+10$. In your second equation, you had the latter term correct but not the former. Your second equation should be $J+10=2(B+10)$.