Fresh juice

The seller offers fresh-squeezed juice, which the customer either pours into his own containers or sells in liter plastic bottles, which the customer buys from him.
A liter of juice costs 40 CZK more than a bottle.
There is no charge for turning the juice into your own container.
When you buy 6 liters of juice, you will pay CZK 312, including a surcharge for six bottles.

1) Calculate in CZK how much you will pay for 5 liters of juice in bottles purchased from the seller.
2) Calculate the percentage of the total price of juice purchased in plastic bottles and the value of the purchased bottle.
Round the result to one decimal place
3) Calculate in CZK how much you will pay for 6 liters of juice poured into your own container.

Correct answer:

a =  260 Kc
b =  11.5 %
x =  276 Kc

Step-by-step explanation:

$$\begin{gathered} c=40+o \\ 6c+6o=312 \\ c=40+o \\ 6\cdot c+6\cdot o=312 \\ c-o=40 \\ 6c+6o=312 \\ Pivot:Row1\leftrightarrow Row2 \\ 6c+6o=312 \\ c-o=40 \\ Row2-\frac{1}{6}\cdot Row1\to Row2 \\ 6c+6o=312 \\ -2o=-12 \\ o=\frac{-12}{-2}=6 \\ c=\frac{312-6o}{6}=\frac{312-6\cdot 6}{6}=46 \\ c=46 \\ o=6 \\ a=5\cdot (c+o)=5\cdot (46+6)=260\text{Kc} \end{gathered}$$

$b=100\cdot \frac{o}{o+c}=100\cdot \frac{6}{6+46}=\frac{150}{13}\%=11.5\%$

$x=6\cdot c=6\cdot 46=276\text{Kc}$

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