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?

Potatobird Jan 11, 2021

#2**+2 **

**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

heureka Jan 11, 2021