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?
Solution:
Let $x$ be the number of copies that would occupy a shelf-length of $5.1 \mathrm{~m}$.
Since the number of copies and the length of the shelf are in direct variation, we have:
$\frac{136}{x}=\frac{3.4}{5.1}$
$\Rightarrow 136 \times 5.1=x \times 3.4$
$\Rightarrow x=\frac{136 \times 5.1}{3.4}$
$=204$
Thus, 204 copies will occupy a shelf of length $5.1 \mathrm{~m}$.