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Answer: Ali is $38$ years old


$$A=\frac {B+31+64+20}{4}=\frac {B+115}{4}\\
\ \\
B=\frac {A+18+54+38}{4}=\frac{A+110}{4}$$
Substitute $B=\dfrac{A+110}{4}$ into $A=\dfrac {B+115}{4}$: $$\begin{align}A&=\dfrac{\frac{A+110}{4}+115}4\\
\ \\
\Rightarrow 4A &= \dfrac{A+110}{4} +115\\
\ \\
\Rightarrow 16A &= A + 110 + 460\\
\Rightarrow 15A &= 570\\
\Rightarrow A &= 38\end{align}$$




This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.