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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
Publisher: Cengage Learning
ISBN: 9781337274203
BuyFind

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
Publisher: Cengage Learning
ISBN: 9781337274203

Solutions

Chapter
Section
Chapter 4.3, Problem 6E
Textbook Problem

Latin Music Sales (Digital) In 2012, total revenues from digital sales of pop/rock, tropical (salsa/merengue/cumbia/bachata), and urban (reggaeton) Latin music in the United States amounted to $24 million. Pop/rock music brought in twice as much as the other two categories combined and $9 million more than tropical music.14 How much revenue was earned from digital sales in each of the three categories?

Expert Solution
To determine

To calculate: The revenue earned from digital sales of pop/rock, tropical and urban music. It is observed that the total revenue earned including all three categories of Latin music is $24 million. Also, pop/rock music brought in twice as much as the other two categories combined and $9 million more than tropical music.

Explanation of Solution

Given Information:

The total revenue earned including all three categories of Latin music is $24 million.

Also, pop/rock music brought in twice as much as the other two categories combined and $9 million more than tropical music.

Formula Used:

Elimination method:

In this method we first combine the equations in a way such that one of the variables gets eliminated. Then we substitute this obtained value in either of the equation to get the value of the other variable.

Calculation:

Let the revenue brought in by each category denoted by variables x,y,z.

Thus,

x is revenue earned through pop/rock music in millions.

y is revenue earned through tropical music in millions.

z is revenue earned through urban music in millions.

The given data shows that the total revenue brought in is $24 million.

Thus, we can say that:

x+y+z=24 …… (1)

The condition says that pop/rock music brought in twice as much as the other two categories combined.

Thus,

x=2(y+z)x=2y+2zx2y2z=0 …… (2)

And pop/rock music also brought in $9 million more than tropical music.

Thus,

x=y+9 …… (3)

Apply the elimination method to find the solution of the given system of the equations:

Begin by multiplying equation (1) with 2 adding to second to eliminate y and z

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Chapter 4 Solutions

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