Question

The sum of the ages of David and Whitney is 69 years. 6 years ago, David's age was 2 timesWhitney's age. How old is David now?

Answer 1

The sum of the ages of David (D) and Whitney (W) is 69 years:

$D+W=69$

6 years ago, David's age was 2 times Whitney's age.

The age of David 6 years ago was (D-6) and the age of Whitney was (W-6).

At that time the age of David was twice the age of Whitney:

$D-6=2(W-6)=2W-12$

Now we can replace the information of the first equation in the second one:

$\begin{gathered} W=69-D \\ D-6=2W-12 \\ D-6=2\mleft(69-D\mright)-12 \\ D-6=138-2D-12 \\ D-6=126-2D \\ D+2D=126+6 \\ 3D=132 \\ D=\frac{132}{3} \\ D=44 \end{gathered}$

David is 44 years old.