Arthur and his son's age

Arthur's age is 50 when he is twice as old as Arthur Jr.

Four years ago Arthur is 11 times as old as his son Arthur Jr,
but four years from now, Arthur will only be 3 times as old as Jr.
What is Arthur’s age when he is twice as old as Arthur Jr?

$\text{Let Arthur $=a$} \\ \text{Let his son Arthur Jr $=j$}$

$\begin{array}{|lrcll|} \hline 1. & \mathbf{a-4} &=& \mathbf{11(j-4)} \\ & a &=& 11(j-4) + 4 \\ & a &=& 11j-44 + 4 \\ & \mathbf{a} &=& \mathbf{11j-40} \\ \hline \end{array}$

$\begin{array}{|lrcll|} \hline 2. & \mathbf{a+4} &=& \mathbf{3(j+4)} \\ & a &=& 3(j+4) - 4 \\ & a &=& 3j+12 - 4 \\ & a &=& 3j+8 \quad | \quad \mathbf{a=11j-40} \\ & 11j-40 &=& 3j+8 \\ & 11j-3j &=& 3j+8+40 \\ & 8j &=& 48 \quad | \quad : 8 \\ & \mathbf{j} &=& \mathbf{6} \\ \hline & \mathbf{a} &=& \mathbf{11j-40} \quad | \quad j=6 \\ & a &=& 11*6 - 40 \\ & a &=& 66-40 \\ & \mathbf{a} &=& \mathbf{26} \\ \hline \end{array}$

$\begin{array}{|lrcll|} \hline 3. & \mathbf{a+x} &=& \mathbf{2(j+x)} \\ & a &=& 2(j+x) - x \\ & a &=& 2j + 2x - x \\ & a &=& 2j + x \\ & x &=& a-2j \quad | \quad a=26~j=6 \\ & x &=& 26-2*6 \\ & x &=& 26-12 \\ & x &=& 14 \\ \hline \end{array}$

14 years from now, Arthur will be $26+14=\mathbf{40}$ years old.
14 years from now, his son Arthur Jr will be $6+14=\mathbf{20}$ years old.
Arthur’s age is then twice as old as Arthur Jr

a = arthur     j = junior

a-4 = 11 (j-4)

a = 11j -40

a+4 = 3 (j+4)

a = 3j +8                      equate the two red equations and solve for j = 6    then a= 3j+8  = 26

26+x = 2 (6+x)    solve for x = 14       Arthur will be 26+14 = 40 y/o   when son is 20 y/0