Bottle, cup and jug

The bottle and the cup have the same weight as the jug. The bottle has the same weight as the cup and plate. Two jugs have the same weight as three plates. What is the weight of the bottle if the weight of the cup is 100g?

Correct answer:

f =  500 g

Step-by-step explanation:

$$\begin{gathered} p=100\text{g} \\ f+p=k \\ f=p+t \\ 2k=3t \\ f+100=k \\ f=100+t \\ 2k=3t \\ f+100=k \\ f=100+t \\ 2\cdot k=3\cdot t \\ f-k=-100 \\ f-t=100 \\ 2k-3t=0 \\ Row2-Row1\to Row2 \\ f-k=-100 \\ k-t=200 \\ 2k-3t=0 \\ Pivot:Row2\leftrightarrow Row3 \\ f-k=-100 \\ 2k-3t=0 \\ k-t=200 \\ Row3-\frac{1}{2}\cdot Row2\to Row3 \\ f-k=-100 \\ 2k-3t=0 \\ 0.5t=200 \\ t=\frac{200}{0.5}=400 \\ k=\frac{0+3t}{2}=\frac{0+3\cdot 400}{2}=600 \\ f=-100+k=-100+600=500 \\ f=500 \\ k=600 \\ t=400 \end{gathered}$$

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