Question

Three students, Neha, Rani, and Sam go to a market to purchase stationery items. Neha buys 4 pens, 3 notepads, and 2 erasers and pays ₹ 60. Rani buys 2 pens, 4 notepads, and 6 erasers for ₹ 90. Sam pays ₹ 70 for 6 pens, 2 notepads, and 3 erasers.
Based upon the above information, answer the following questions:

(i) Form the equations required to solve the problem of finding the price of each item, and express it in the matrix form \( A \mathbf{X} = B \).

Answer 1

Let the price of each item be:

• \( x_1 \) for the price of one pen,
• \( x_2 \) for the price of one notepad,
• \( x_3 \) for the price of one eraser.

The information given can be converted into the following system of equations: \[ 4x_1 + 3x_2 + 2x_3 = 60 \quad \text{(Neha's purchase)} \] \[ 2x_1 + 4x_2 + 6x_3 = 90 \quad \text{(Rani's purchase)} \] \[ 6x_1 + 2x_2 + 3x_3 = 70 \quad \text{(Sam's purchase)} \] This system can be written in matrix form as: \[ \begin{pmatrix} 4 & 3 & 2 \\ 2 & 4 & 6 \\ 6 & 2 & 3 \end{pmatrix} \begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} = \begin{pmatrix} 60 \\ 90 \\ 70 \end{pmatrix} \]