Chuck

Chuck Stone has 8 7/8 cubic yards of concrete in a truck. How much concrete remains in the truck if he unloads 2 1/2 cubic yards at the first stop, 3 cubic yards at the second stop, and 1 3/4 cubic yards at the third stop?

Correct answer:

x =  1 ⁵⁄₈ = 13/8 yd³

Step-by-step explanation:

$$\begin{gathered} a=8\frac{7}{8}=8+\frac{7}{8}=\frac{8\cdot 8+7}{8}=\frac{64+7}{8}=\frac{71}{8}=8.875{\text{yd}}^3 \\ b=2\frac{1}{2}=2+\frac{1}{2}=\frac{2\cdot 2+1}{2}=\frac{4+1}{2}=\frac{5}{2}=2.5{\text{yd}}^3 \\ c=3{\text{yd}}^3 \\ d=1\frac{3}{4}=1+\frac{3}{4}=\frac{1\cdot 4+3}{4}=\frac{4+3}{4}=\frac{7}{4}=1.75{\text{yd}}^3 \\ w=b+c+d=\frac{5}{2}+3+\frac{7}{4}=\frac{29}{4}=7.25{\text{yd}}^3 \\ x=a-w=\frac{71}{8}-\frac{29}{4}=\frac{71}{8}-\frac{58}{8}=\frac{71-58}{8}=\frac{13}{8}=\frac{13}{8}{\text{yd}}^3=1\frac{5}{8}{\text{yd}}^3=1.625{\text{yd}}^3 \end{gathered}$$

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