A textile

A textile store sold a bolt of denim (what jeans are made of). One day, the store purchased the following lengths from the factory: 5 2/3, 7, 4 2/3, 8 5/8, 9 3/5, 10 ½, and 8 yards. How many yards were sold?

Correct answer:

x =  54 ⁷⁄₁₂₀ = 6487/120 yd

Step-by-step explanation:

$$\begin{gathered} a=5\frac{2}{3}=5+\frac{2}{3}=\frac{5\cdot 3+2}{3}=\frac{15+2}{3}=\frac{17}{3}\doteq 5.6667\text{yd} \\ b=7\text{yd} \\ c=4\frac{2}{3}=4+\frac{2}{3}=\frac{4\cdot 3+2}{3}=\frac{12+2}{3}=\frac{14}{3}\doteq 4.6667\text{yd} \\ d=8\frac{5}{8}=8+\frac{5}{8}=\frac{8\cdot 8+5}{8}=\frac{64+5}{8}=\frac{69}{8}=8.625\text{yd} \\ e=9\frac{3}{5}=9+\frac{3}{5}=\frac{9\cdot 5+3}{5}=\frac{45+3}{5}=\frac{48}{5}=9.6\text{yd} \\ f=10\frac{1}{2}=10+\frac{1}{2}=\frac{10\cdot 2+1}{2}=\frac{20+1}{2}=\frac{21}{2}=10.5\text{yd} \\ g=8\text{yd} \\ x=a+b+c+d+e+f+g=\frac{17}{3}+7+\frac{14}{3}+\frac{69}{8}+\frac{48}{5}+\frac{21}{2}+8=\frac{6487}{120}\text{yd}=54\frac{7}{120}\text{yd}=54.0583\text{yd} \end{gathered}$$

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