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CalculusFinite Mathematics and Applied Calculus (MindTap Course List)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?BuyFind*arrow_forward*

7th Edition

Stefan Waner + 1 other

Publisher: Cengage Learning

ISBN: 9781337274203

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.

**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

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:

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

Thus,

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

Thus,

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*

Finite Mathematics and Applied Calculus (MindTap Course List)

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