Question

68 boxes of a certain commodity require a shelf-length of 13.6 m. How many boxes of the same commodity would occupy a shelf length of 20.4 m?

Answer 1

Number of Boxes	68	x
Shelf-length (in m)	13.6	20.4

Let x be the number of boxes that occupy a shelf-length of 20.4 m.

$$\begin{gathered} \mathrm{If}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{shelf}\mathrm{increases},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{boxes}\mathrm{will}\mathrm{also}\mathrm{increase}. \\ \mathrm{Therefore},\mathrm{it}\mathrm{is}\mathrm{a}\mathrm{case}\mathrm{of}\mathrm{direct}\mathrm{variation}. \\ \frac{68}{x}=\frac{13.6}{20.4} \\ \Rightarrow 68\times 20.4=x\times 13.6 \\ \Rightarrow x=\frac{68\times 20.4}{13.6} \\ =\frac{1387.2}{13.6} \\ =102 \\ \mathrm{Thus},102\mathrm{boxes}\mathrm{will}\mathrm{occupy}\mathrm{a}\mathrm{shelf}-\mathrm{length}\mathrm{of}20.4\mathrm{m}. \end{gathered}$$