4 tables and 3 chairs, together, cost Rs 2,250 and 3 tables and 4 chairs cost Rs 1950.
Question:

4 tables and 3 chairs, together, cost Rs 2,250 and 3 tables and 4 chairs cost Rs 1950. Find the cost of 2 chairs and 1 table.

Solution:

Given:

(i) Cost of 4 tables and 3 chairs = Rs 2250.

(ii) Cost of 3 tables and 4 chairs = Rs 1950.

To find: The cost of 2 chairs and 1 table.

Suppose, the cost of 1 table = Rs x.

The cost of 1 chair = Rs y.

According to the given conditions,

4x + 3y = 2250,

4x + 3y − 2200 = 0 …… (1)

3x + 4y = 1950,

3x + 4y − 1950 = 0 …… (2)

Solving eq. (1) and Eq. (2) by cross multiplication

$\frac{x}{-5850+9000}=\frac{-y}{-7800+6750}=\frac{1}{16-9}$

$\frac{x}{3150}=\frac{-y}{-1050}=\frac{1}{7}$

$x=\frac{3150}{7}$

$=450$

$\therefore$ cost of 1 table $=$ Rs. 450

cost of 1 table $=$ Rs. 450

$y=\frac{1050}{7}$

$=150$

$\therefore \cos t$ of 1 chairs $=$ Rs. 150 .

cost of 2 chairs $=$ Rs. 300

Hence total cost of 2 chairs and 1 table $=$