Barrels

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

Final Answer:

a =  7
b =  14
c =  21

Step-by-step explanation:

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

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

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

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