Question

In a library 136 copies of a certain book require a shelf-length of 3.4 metre. How many copies of the same book would occupy a shelf-length of 5.1 metres?

Answer 1

Number of copies	136	x
Length the shelf (in m)	3.4	5.1

Let x be the number of copies that would occupy a shelf-length of 5.1 m.

$$\begin{gathered} \mathrm{Since}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{copies}\mathrm{and}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{shelf}\mathrm{are}\mathrm{in}\mathrm{direct}\mathrm{variation},\mathrm{we}\mathrm{have}: \\ \frac{136}{x}=\frac{3.4}{5.1} \\ \Rightarrow 136\times 5.1=x\times 3.4 \\ \Rightarrow x=\frac{136\times 5.1}{3.4} \\ =204 \\ \mathrm{Thus},204\mathrm{copies}\mathrm{will}\mathrm{occupy}\mathrm{a}\mathrm{shelf}\mathrm{of}\mathrm{length}5.1\mathrm{m}. \end{gathered}$$