Question

The cost of 2 books, 6 notebooks and 3 pens is  Rs 40. The cost of 3 books, 4 notebooks and 2 pens is Rs 35, while the cost of 5 books, 7 notebooks and 4 pens is Rs 61. Using this information and matrix method, find the cost of 1 book, 1 notebook and 1 pen separately.

Answer 1

Let the cost of 1 book, 1 notebook and 1 pen be Rs x, Rs y and Rs z respectively.

According to the given conditions,

2x + 6y + 3z = 40

3x + 4y + 2z = 35

5x + 7y + 4z = 61

These equations can be written in the matrix form as

By equality of matrices,\

x − 2y − z = −5 ….(i)

y + z/2= 5 ….(ii)

z/2 = 1 ….(iii)

From (iii), z = 2

Putting z = 2 in (ii), we get

y + 1 = 5

∴ y = 4

Putting y = 4, z = 2 in (i), we get

x − 8 − 2 = − 5

∴ x = 5

Thus, the cost of 1 book, 1 notebook and 1 pen are 5, 4 and 2 respectively