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Two box types $$A$$ and $$B$$ hold $$38$$ and $$20$$ candles respectively. Exactly $$288$$ candles fill all the boxes. If $$m$$ boxes are of type $$A$$ and $$n$$ boxes are of type $$B$$, then $$\frac{m}{n}$$ is
The equation is $$38m+20n=288$$, or $$19m+10n=144$$. The positive integer solution is $$m=6$$ and $$n=3$$. Therefore, $$\frac{m}{n}=\frac{6}{3}=2$$.
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