Question

Set up a table and solve the following problems. Use unitary method to verify the answer.
If the thickness of a pile of $12$ cardboards is $35mm$ , find the thickness of a pile of $294$ cardboards.

Answer 1

Draw a table and find the thickness

Given: Thickness of a pile of $12$ cardboards $=35mm$
Let the thickness of pile of $294$ cardboards be ${}^{\prime }{x}^{\prime }mm$

Thickness $\left(mm\right)$	$35$	$x$
No. of cardboards	$12$	$294$

Clearly, more the number of cardboards, more will be the thickness of pile of those cardboards. So, it is a case of direct variation.

Therefore, ratio of the thickness to the number of cardboards would be same for both the cases.

$\Rightarrow \frac{35}{12}=\frac{x}{294}$

$\Rightarrow x=294\times \frac{35}{12}$

$\Rightarrow x=857.5$

Thus, the thickness of pile is $857.5mm$ or $85.75cm$
$(\because 1cm=10mm)$

Hence, the thickness of a pile of $294$ cardboards is $857.5mm$ or $85.75cm$.

Verify using unitary method

Given: Thickness of a pile of $12$ cardboards $=35mm$

$\Rightarrow$ Thickness of a pile of $1$ cardboard $=\frac{35}{12}mm$

$\Rightarrow$ Thickness of a pile of $294$ cardboards

$=\frac{35}{12}\times 294$

$=857.5mm$

Thus, the thickness of pile is $857.5mm$ or $85.75cm$
$\because 1cm=10mm$

Hence, verified.