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 result:

x =  12

Solution:

$z=12a \ \\ z=18b \ \\ z - 4a -4b=b \cdot \ x \ \\ \ \\ z - 4(z/12)-4 \cdot \ (z/18)=(z/18) \cdot \ (x-4) \ \\ \ \\ \ \\ 1 - 4 \cdot \ (1/12) - 4 \cdot \ (1/18)=1/18 \cdot \ (x-4) \ \\ \ \\ 2x=24 \ \\ \ \\ x=12$

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