Five-sevenths of a volume

Forty-two liters of water fill the barrel to two-thirds of its volume. If it is filled to five-sevenths of a volume, how many liters of water do we need to add?

Correct answer:

x =  3 l

Step-by-step explanation:

$$\begin{gathered} 42=\frac{2}{3}V \\ 42=2/3\cdot V \\ 2V=126 \\ V=\frac{126}{2}=63 \\ V=63 \\ 42+x=\frac{5}{7}\cdot V \\ 42+x=\frac{5}{7}\cdot 63 \\ 42+x=5/7\cdot 63 \\ 7x=21 \\ x=\frac{21}{7}=3 \\ x=3=3\text{l} \end{gathered}$$

Try another example