A trail mix

Diego is making a trail mix for him and his friends to take with them on a hike next week. He mixes 4 2/6 pounds of mixed nuts, 3 3/6 pounds of peanuts, and 2 3/6 pounds of chocolate chips. How many 1/3-pound bags of trail mix can he make?

Correct answer:

n =  31

Step-by-step explanation:

$$\begin{gathered} a=4\frac{2}{6}=4+\frac{2}{6}=\frac{4\cdot 6+2}{6}=\frac{24+2}{6}=\frac{26}{6}=\frac{13}{3}=4\frac{1}{3}\doteq 4.3333\text{lb} \\ b=3\frac{3}{6}=3+\frac{3}{6}=\frac{3\cdot 6+3}{6}=\frac{18+3}{6}=\frac{21}{6}=\frac{7}{2}=3\frac{1}{2}=3.5\text{lb} \\ c=2\frac{3}{6}=2+\frac{3}{6}=\frac{2\cdot 6+3}{6}=\frac{12+3}{6}=\frac{15}{6}=\frac{5}{2}=2\frac{1}{2}=2.5\text{lb} \\ s=a+b+c=\frac{13}{3}+\frac{7}{2}+\frac{5}{2}=\frac{26}{6}+\frac{21}{6}+\frac{15}{6}=\frac{26+21+15}{6}=\frac{62}{6}=\frac{31}{3}=10\frac{1}{3}\doteq 10.3333\text{lb} \\ m=1/3=\frac{1}{3}\doteq 0.3333\text{lb} \\ n=s/m=\frac{31}{3}/\frac{1}{3}=\frac{31}{3}:\frac{1}{3}=\frac{31}{3}\cdot \frac{3}{1}=\frac{31\cdot 3}{3\cdot 1}=\frac{93}{3}=31 \end{gathered}$$

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