Question

$4$ chairs and $3$ tables cost Rs. $2100$ and $5$ chairs and $2$ tables cost Rs. $1750$. Find the cost of a chair and a table separately.

Answer 1

Let the cost of a chair be $Rs.x$ and that of a table be $Rs.y$. Then,
$4x+3y=2100$
and, $5x+2y=1750$

This system of equations can be written as
$4x+3y-2100=0$
$5x+2y-1750=0$

By using cross-multiplication, we have
$\frac{x}{3\times -1750-2\times -2100}=\frac{-y}{4\times -1750-5\times -2100}=\frac{1}{4\times 2-3\times 5}$

$\Rightarrow \frac{x}{-5250+4200}=\frac{-y}{-7000+10500}=\frac{1}{8-15}$

$\Rightarrow \frac{x}{-1050}=\frac{y}{-3500}=\frac{1}{-7}$

$\Rightarrow x=\frac{-1050}{-7}=150$ and $y=\frac{-3500}{-7}=500$.

$\therefore$ cost of the 1 chair is $Rs150$ and the cost of 1 table is $Rs500$.