Question

$2$ tables and $3$ chairs together cost Rs. $2000$ whereas $3$ tables and $2$ chairs together cost Rs. $2500$. Find the total cost of $1$ table and $5$ chairs.

Answer 1

Let the cost of a table be Rs x and that of a chair be Rs y. Then,
$2x+3y=2000$
and, $3x+2y=2500$

This system of equations may be written as
$2x+3y-2000=0$
$3x+2y-2500=0$

By using cross-multiplication, we get

$\frac{x}{3\times -2500-2\times -2000}=\frac{-y}{2\times -2500-3\times -2000}=\frac{1}{2\times 2-3\times 3}$

$\Rightarrow \frac{x}{-7500+4000}=\frac{-y}{-5000+6000}=\frac{1}{4-9}$

$\Rightarrow \frac{x}{-3500}=\frac{y}{-1000}=\frac{1}{-5}$

$\Rightarrow x=\frac{-3500}{-5}=700$ and $y=\frac{-1000}{-5}=200$

$\therefore$ Cost of a table $=$Rs. $700$ and, cost of a chair $=$Rs. $200$

Hence, cost of one table and $5$ chairs $=$Rs. $(x+5y)=$Rs. $1700$.