Question

The cost of 4 pencils ,3 pens and 2 books is Rs.150.The coat of 1 pencil and 3 books is Rs.125.The cost of 6 pencils ,2 pens and 3 books is Rs.175.Find the cost of each item by using matrices

Answer 1

Given :

The cost of 4 pencils , 3 pens and 2 books is Rs 150

The cost of 1 pencil and 3 books is Rs 125

The cost of 6 pencils , 2 pens and 3 books is Rs 175

To Find :

The cost of each item by using matrices

Solution :

Let The cost of each pencil = x

     The cost of each pen = y

     The cost of each books = z

∵ The cost of 4 pencils , 3 pens and 2 books is Rs 150

Or,   4 x + 3 y + 2 z = 150                      ...........1

The cost of 1 pencil and 3 books is Rs 125

Or,    1 x + 3 z = 125                               ...........2

The cost of 6 pencils , 2 pens and 3 books is Rs 175

Or,    6 x + 2 y + 3 z = 175                      ..........3

Solving eq 3 and 2

   (  6 x + 2 y + 3 z ) - (   1 x + 3 z ) = 175 - 125

Or,   5 x + 2 y = 50                                ..........4

Solving eq 1 and 2

3 × ( 4 x + 3 y + 2 z ) - 2 × ( 1 x + 3 z ) =  3 × 150 -  2 × 125

Or,   ( 12 x - 2 x ) + ( 9 y ) + ( 6 z - 6 z ) = 450 - 250

Or,    10 x + 9 y + 0 = 200

Or,   10 x + 9 y = 200                          .........5

Solving eq 4 and 5

   ( 10 x + 9 y ) - 2 × ( 5 x + 2 y ) = 200 - 2 × 100

Or,   5 y = 100

∴         y = $\dfrac{100}{5}$  = 20

So, The cost pens = y = Rs 20

Put the value of y into eq 4

     5 x + 2 × 20 = 50

Or,   5 x + 40 = 50

Or,  5 x = 50 - 40

Or,   5 x = 10

∴         x = $\dfrac{10}{5}$ = 2

So, The cost pencils = x = Rs 2

Put the value of x , y into eq 1

   4 x + 3 y + 2 z = 150  

Or,   4 × 2 + 3 × 20 + 2 × z = 150  

Or,   8 + 40 + 2 × z = 150  

Or,   2 × z = 150 - 48

Or,   2 × z = 102

∴            z = $\dfrac{102}{2}$ = 51

So, The cost books = z = Rs 51

Hence,

The cost pencils Rs 2

The cost pens  Rs 20

The cost books Rs 51  . Answer