Barrels

Peter has 42 barrels. One-sixth of them are filled with lemonade, one third is filled with wine and half is empty. Calculate how many barrels are with each filling.

Correct result:

a =  7
b =  14
c =  21

Solution:

$$\begin{gathered} n=42 \\ a={\displaystyle \frac{1}{6}}\cdot n={\displaystyle \frac{1}{6}}\cdot 42=7 \end{gathered}$$

$b={\displaystyle \frac{1}{3}}\cdot n={\displaystyle \frac{1}{3}}\cdot 42=14$

$$\begin{gathered} c={\displaystyle \frac{1}{2}}\cdot n={\displaystyle \frac{1}{2}}\cdot 42=21 \\ x={\displaystyle \frac{1}{6}}+{\displaystyle \frac{1}{3}}+{\displaystyle \frac{1}{2}}=1 \end{gathered}$$

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