Given the details of stock of various types of books.
Physics: 10 dozen books
Chemistry: 8 dozen books
Mathematics: 5 dozen books
Hence, the number of dozens of books available in the store can be represented in matrix form with each column corresponding to a different subject as -
The price of each of the items is also given.
Cost of one physics book = Rs 8.30
⇒ Cost of one dozen physics books = 12 × Rs 8.30
∴ Cost of one dozen physics books = Rs 99.60
Cost of one chemistry book = Rs 3.45
⇒ Cost of one dozen chemistry books = 12 × Rs 3.45
∴ Cost of one dozen chemistry books = Rs 41.40
Cost of one mathematics book = Rs 4.50
⇒ Cost of one dozen mathematics books = 12 × Rs 4.50
∴ Cost of one dozen mathematics books = Rs 54
Hence, the cost of purchasing a dozen books of each subject can be represented in matrix form with each row corresponding to a different subject as –
Now, the amount received by the store upon selling all the available books can be found by taking the product of the matrices X and Y.
⇒ XY = [10 × 99.60 + 8 × 41.40 + 5 × 54]
⇒ XY = [996 + 331.20 + 270]
∴ XY = [1597.20]
Thus, the total amount the store will receive from selling all the items is Rs 1597.20.
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