The barrel

The barrel is 135 cm high. If we fill it to a height of 60 cm and it weighs 163 kg. If we fill it to a height of 80 cm, it weighs 213 kg. How many kg weighs a full and how much empty barrel?

Correct answer:

f =  350.5 kg
b =  13 kg

Step-by-step explanation:

$$\begin{gathered} h=135\text{ cm } \\ {m}_1=163\text{ kg } \\ {m}_2=213\text{ kg } \\ {q}_1={\displaystyle \frac{60}{h}}={\displaystyle \frac{60}{135}}={\displaystyle \frac{4}{9}}\doteq 0.4444 \\ {q}_2={\displaystyle \frac{80}{h}}={\displaystyle \frac{80}{135}}={\displaystyle \frac{16}{27}}\doteq 0.5926 \\ {q}_1\cdot a+b=m_1 \\ {q}_2\cdot a+b=m_2 \\ 0.44444444444444\cdot a+b=163 \\ 0.59259259259259\cdot a+b=213 \\ 0.444444a+b=163 \\ 0.592593a+b=213 \\ a={\displaystyle \frac{675}{2}}\doteq 337.5 \\ b=13 \\ f=a+b=337.5+13={\displaystyle \frac{701}{2}}={\displaystyle \frac{701}{2}}\text{ kg}=350.5\text{ kg} \end{gathered}$$

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