Question

$4$ chairs and $3$ tables cost $Rs.2100$ and $5$ chairs and $2$ tables cost $Rs.1750$. Find the cost of $1$ chair and $1$ table separately.

Answer 1

Let cost of one chair $=x$

Let cost of one table $=y$

$4x+3y=2100$

$5x+2y=1750$

Solving $\left(i\right)$ and $\left(ii\right)$

Solving by cross multiplication

$a_{1}x+b_{1}y+c_1=0$

$a_{2}x+b_{2}y+c_2=0$

$\Rightarrow \frac{x}{b_1{c}_2-b_2{c}_1}=\frac{y}{c_1{a}_2-c_2{a}_1}=\frac{1}{a_1{b}_2-a_2{b}_1}$

$\Rightarrow \frac{x}{3\times (-1750)-2\times (-2100)}=\frac{y}{(-2100)\times 5-(-1750)\times 4}=\frac{1}{4\times 2-5\times 3}$
$\Rightarrow \frac{x}{-1050}=\frac{y}{-3500}=\frac{1}{-7}$

$\Rightarrow x=150,y=500$

So cost of one chair $=Rs.150$ and cost of one table $=Rs.500$