Dana and sandbox

Dana helped her dad build a sandbox for her younger sister. The sandbox is shaped like a rectangular prism, 4 1/2 feet long and 4 feet wide. Dana used bags of sand to fill the sandbox 1/2 of a foot deep. Each bag contained 1/2 of a cubic foot of sand. How many bags must she buy?

Correct answer:

n =  18

Step-by-step explanation:

$$\begin{gathered} a=4\frac{1}{2}=4+\frac{1}{2}=\frac{4\cdot 2+1}{2}=\frac{8+1}{2}=\frac{9}{2}=4\frac{1}{2}=4.5\text{ft} \\ b=4\text{ft} \\ c=\frac{1}{2}=0.5\text{ft} \\ {V}_1=\frac{1}{2}=0.5{\text{ft}}^3 \\ V=a\cdot b\cdot c=\frac{9}{2}\cdot 4\cdot \frac{1}{2}=9{\text{ft}}^3 \\ {n}_1=V/V_1=9/\frac{1}{2}=9:\frac{1}{2}=9\cdot \frac{2}{1}=\frac{9\cdot 2}{1}=\frac{18}{1}=18 \\ n=\lceil n_1\rceil =\lceil 18\rceil =18 \end{gathered}$$

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