The coal

The coal stock would be enough to heat a larger room for 12 weeks and a smaller one for 18 weeks. It was heated for four weeks in both rooms, then only in a smaller one. How long was the coal stock enough?

Correct answer:

x =  12

Step-by-step explanation:

$$\begin{gathered} z=12a \\ z=18b \\ z-4a-4b=b\cdot x \\ z-4(z/12)-4\cdot (z/18)=(z/18)\cdot (x-4) \\ 1-4\cdot (1/12)-4\cdot (1/18)=1/18\cdot (x-4) \\ 2x=24 \\ x=\frac{24}{2}=12 \\ x=12 \end{gathered}$$

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