A barrel

A barrel of sorghum weighs 56kg. The same barrel filled with kerosene weighs 35kg. If sorghum is twice as heavy as kerosene, how much does the empty barrel weigh?

Final Answer:

b =  14 kg

Step-by-step explanation:

$$\begin{gathered} b+s=56kg \\ b+k=35kg \\ s=2k \\ b+2k=56 \\ b+k=35 \\ b+2\cdot k=56 \\ b+k=35 \\ b+2k=56 \\ b+k=35 \\ Row2-Row1\to Row2 \\ b+2k=56 \\ -k=-21 \\ k=\frac{-21}{-1}=21 \\ b=56-2k=56-2\cdot 21=14=14\text{kg} \\ b=14 \\ k=21 \\ \text{ Verifying Solution: } \\ s=2\cdot k=2\cdot 21=42\text{kg} \\ {m}_1=b+s=14+42=56\text{kg} \\ {m}_2=b+k=14+21=35\text{kg} \end{gathered}$$

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