Tank - fuel prices

I have a car with a 50l tank. My task is to find out the price of a full tank of fuel by weighted average at the end of the year. In December, 30l of fuel was filled - 37.50 CZK, and in November 40l - 38.40 CZK. What is the price per 1 liter and the value of a full tank by weighted average?

Correct answer:

c =  38.0143 Kc/l
x =  1900.7143 Kc

Step-by-step explanation:

$$\begin{gathered} V=50\text{l} \\ {V}_1=30\text{l} \\ {c}_1=37.50\text{Kc/l} \\ {V}_2=40\text{l} \\ {c}_2=38.40\text{Kc/l} \\ c=\frac{V_1\cdot c_1+V_2\cdot c_2}{V_1+V_2}=\frac{30\cdot 37.5+40\cdot 38.4}{30+40}=38.0143\text{Kc/l} \end{gathered}$$

$x=c\cdot V=38.0143\cdot 50=1900.7143\text{Kc}$

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