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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.
Solution
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
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