Question

$3$ chairs and $2$ tables costs $Rs.700$ and $5$ chairs and $3$ tables costs $Rs.1100$. What is the cost of $2$ chairs and $2$ tables?

Answer 1

Let $x$ be the cost of a chair and $y$ be the cost of a table.

So, according to the question, the required equations are:

$3x+2y=700$…(i)

$5x+3y=1100$ …(ii)

Multiply (i) by $5$ and (ii) by $3$

$15x+10y=3500$ …(iii)

$15x+9y=3300$ …(iv)

Subracting (iii) from (iv)

we get, $y=200$

Put value $y$ in (i)

$\begin{array}{rcl}3x+400& =& 700\\ 3x& =& 300\\ x& =& 100\end{array}$

The cost of $2$ chairs and $2$ tables $=2x+2y$

$$\begin{gathered} =200+400 \\ =600 \end{gathered}$$

Hence, the cost of $2$ chairs and $2$ tables is $Rs.600$.