Question:
If the thickness of a pile of 12 cardboards is 35 mm, find the thickness of a pile of 294 cardboards.
Solution:
Let x cm be the thickness of a pile of 294 cardboards.
Since the pile of the cardboards and its thickness are in direct variation, we have:
$\frac{3.5}{x}=\frac{12}{294}$
$\Rightarrow 3.5 \times 294=x \times 12$
$\Rightarrow x=\frac{3.5 \times 294}{12}$
$=\frac{1029}{12}$
$=85.75 \mathrm{~cm}$
Thus, the thickness of a pile of 294 cardboards will be $85.75 \mathrm{~cm}($ or $857.5 \mathrm{~mm})$.
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