Question

The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs. 80, Rs. 60 and Rs. 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.

Answer 1

Hint: Here, it is given that all the details are in dozens, we know that a dozen consists of 12 items. So firstly, find the numbers of books in chemistry, physics and economics. Then multiply the price with them to find the selling price of all the books using matrix algebra method.

Complete step-by-step answer:
The number of chemistry books in the bookshop is $ 10\;{\rm{dozen}} $ .
The number of physics books in the bookshop is \[8\;{\rm{dozen}}\].
The number of economics books in the bookshop is \[10\;{\rm{dozen}}\].
It is given that the selling price of each chemistry book is \[p = 80\].
It is given that the selling price of each physics book is \[q = 60\].
It is given that the selling price of each economics book is \[r = 40\].
We know number of chemistry book in the bookshop is given by,
\[10 \times 12 = 120\]
We know number of physics book in the bookshop is given by,
\[8 \times 12 = 96\]
We know number of economics book in the bookshop is given by,
\[10 \times 12 = 120\]
Now, the matrix algebra method to find the selling price of all the books will be,
\[M = \left[ {x\,\,\,y\,\,\,z} \right]\left[ \begin{array}{l}
p\\
q\\
r
\end{array} \right]\]
On substituting the values in the above equation, then we get,
\[\begin{array}{c}
M = \left[ {120\,\,\,96\,\,\,\,120} \right]\left[ \begin{array}{l}
80\\
60\\
40
\end{array} \right]\\
 = 120 \times 80 + 96 \times 60 + 120 \times 40\\
 = 9600 + 5760 + 4800\\
 = {\rm{Rs}}\,20160
\end{array}\]
Therefore, the price of the 120 chemistry books, 96 physics books and 120 economics books is 20160.

Note: In this solution, it is asked that to find the price of all the books in matrix algebra method, as we know we have to care about taking the matrix form, the matrix may be \[m \times n\], it means the number of rows and columns are denoted as \[m \times n\], so we have to sure about the rows and columns. The matrix of the books should be \[1 \times 3\] and the matrix of the prices of books should be quite opposite to it \[3 \times 1\].