Question

Three chairs and two tables cost ₹ 1850. Five chairs and three tables cost ₹2850. Find the cost of four chairs and one table by using matrices

Answer 1

Let the cost of 1 chair and 1 table be ₹ x and ₹ y respectively.

According to the first condition,

3x + 2y = 1850

According to the second condition,

5x + 3y = 2850

Matrix form of the above system of equations is

`[(3, 2),(5, 3)] [(x),(y)] = [(1850),(2850)]`

Applying R₂ → 3R₂ − 5R₁, we get

`[(3, 2),(0, -1)] [(x),(y)] = [(1850),(-700)]`

∴ By equality of matrices, we get

3x + 2y = 1850    .......(i)

−y = −700

i.e., y = 700

Substituting y = 700 in equation (i), we get

3x + 2(700) = 1850

∴ 3x = 450

∴ x = 150

∴ The cost of four chairs = 4 × 150 = ₹ 600

∴ The cost of four chairs and one table is ₹ 600 + ₹ 700 = ₹ 1300.