Gift box

A gift box has dimensions of: 8 1/2 inches, 5 1/2 inches, and 2 1/2 inches, respectively. How many cubes with side lengths of 1/2 inches would be needed to fill the gift box?

Correct answer:

n =  935

Step-by-step explanation:

$$\begin{gathered} x=8{\displaystyle \frac{1}{2}}=8+{\displaystyle \frac{1}{2}}={\displaystyle \frac{8\cdot 2+1}{2}}={\displaystyle \frac{17}{2}}=8.5\text{ in } \\ y=5{\displaystyle \frac{1}{2}}=5+{\displaystyle \frac{1}{2}}={\displaystyle \frac{5\cdot 2+1}{2}}={\displaystyle \frac{11}{2}}=5.5\text{ in } \\ z=2{\displaystyle \frac{1}{2}}=2+{\displaystyle \frac{1}{2}}={\displaystyle \frac{2\cdot 2+1}{2}}={\displaystyle \frac{5}{2}}=2.5\text{ in } \\ a={\displaystyle \frac{1}{2}}=0.5\text{ in } \\ {n}_1=x\mathrm{/}a=8.5\mathrm{/}0.5=17 \\ {n}_2=y\mathrm{/}a=5.5\mathrm{/}0.5=11 \\ {n}_3=z\mathrm{/}a=2.5\mathrm{/}0.5=5 \\ n=n_1\cdot n_2\cdot n_3=17\cdot 11\cdot 5=935 \end{gathered}$$

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