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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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Chapter
Section
BuyFindarrow_forward

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Sales As the buyer at OHaganBooks.com, you are planning to increase stocks of books about music, and have been monitoring worldwide sales. Last year, worldwide sales of books about rock, rap, and classical music amounted to $5.8 billion. Books on rock music brought in twice as much revenue as books on rap music and they brought in 900% the revenue of books on classical music. How much revenue was earned in each of the three categories of books?

To determine

To calculate: The revenue earned in each of the three categories of books which are rock, rap and classical music respectively.

Explanation

Given Information:

As the buyer at OHaganBooks.com, you are planning to increase stocks of books about music, and have been monitoring worldwide sales. Last year, worldwide sales of books about rock, rap and classical music amounted to $5.8billion. Books on rock music brought in twice as much revenue as books on rap music and they brought in 900% the revenue of books on classical music.

Formula Used:

Elementary row operations:

Type 1: Replacing the row Ri by aRi, where a is a nonzero number.

Type 2: Replacing the row Ri by aRi±bRj, where a is a nonzero number.

Gauss-Jordan reduction method:

Step 1: First by using operations of type 1 clear the fractions or decimals if any.

Step 2: Now select the first nonzero element of the first row as pivot element.

Step 3: Use the pivot to clear its column using operations of type 2.

Step 4: Select the first nonzero element in the second row a pivot and clear its column.

Step 5: Select the first nonzero element in the third row a pivot and clear its column.

Step 6: Turn all the selected pivot elements into a 1 using operations of type 1.

Calculation:

Firstly, identify and label the unknowns.

Considering the provided information, the unknowns should be labelled like this,

x be Revenue earned from books on rock music

y be Revenue earned from books on rap music

z be Revenue earned from books on classical music

It is known that the total revenue from the books on rock, rap and classical music is amounted to $5.8 billion.

x+y+z=5.8

Now, we are provided that the revenue earned from books on rock music is twice the revenue earned from books on rap music, which can be represented as,

x=2yx2y=0

From the information provided we know that the revenue earned form the books on rock music is 900% more or 9 times the revenue earned from the books on classical music. This can be written in the form of equation as,

x=9zx9z=0

The augmented matrix for the obtained equations is:

[1115.812001090]

Apply Gauss Jordan reduction method to get the solution of the given system of equation.

Begin by clearing the fraction in the rows of the matrix by the operation R15R1

[1115.812001090][5552912001090]

Now, pivot the first nonzero element of first row and clear its column

Perform the operation R25R2R1,R35R3R1,

[5552912001090][55529015529055029]

Now, pivot the first nonzero element of second row and clear its column.

Perform the operation R13R1+R2,R33R3R2,

[5552912001090][15010580155290014558]

Simplify the third row by the operation R3129R3

[15010580155290014558][15010580155290052]

Now, select the first nonzero element of third row and clear its column

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