The coal

The coal stock would be enough to heat a larger room for 12 weeks, 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:

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

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