Question

Suppose in one year, total revenues from digital sales of pop/rock, tropical (salsa/merengue/cumbia/bachata), and urban (reggaeton) Latin music in a certain country amounted to $21 million. Pop/rock music brought in twice as much as the other two categories combined and $10 million more than tropical music. How much revenue was earned from digital sales in each of the three categories?

Answer 1

Answer:

• Pop/Rock sold $14 million
• Tropical music sold $3 million
• Reggaeton sold $4 million.

Step-by-step explanation:

First let's write the music genre as follows:

• X = Pop/Rock
• Y = Tropical
• Z = Reggaeton

$\left \bigg \{ {{X + Y + Z = 21 (1) } \atop {X=2(Y + Z) (2)}} \text{; }  \left \bigg \{ {{X + Y + Z = 21 (1)} \atop {X= Z + 10  (3)}$

Let's use $(2)$ in $(1)$:

$X + Y + Z = 21 \Rightarrow 2(Y + Z) + Y + Z = 21 \Rightarrow\\3(Y+Z) = 21 \Rightarrow Y+Z = 7$

Then,

$X + 7 = 21 \Righarrow X = 14$

Now let's solve for Z,

$14 = Z +10 \Rightarrow Z = 4$

Finally, let's solve for Y,

$14 = 2(Y + 4) \Rightarrow Y + 4 = 7 \Rightarrow Y = 3$

So Pop/Rock sold $14 million, Tropical music sold $3 million and Reggaeton sold $4 million.

Answer 2

You can use the fact given that pop/rock music is twice as much as the other two categories combined and $10 million more than tropical music to form the equations to find the revenue earned by each of the three categories.

The revenue earned by each of the three categories is

• Pop/rock: $10,500,000
• Tropical: $500,000
• Latin: $10,000,000

How to form mathematical expression from the given description?

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

How to get revenue earned by each music category?

(For the given context)

• Let the tropical music earned 'x' amount from digital sale.
• Let the Latin music earned 'y' amount from digital sale.
• Let the pop/rock music earned 'z' amount from digital sale

Then, by given description, we have:

Pop/rock music brought in twice as much as the other two combined

or

$z = x + y$

Pop/rock music brought in $10 million more than tropical music

$z = 10,000,000 + x$

And that all of them together earned $21 million

or

$x + y + z = 21,000,000$

Putting value of z in second equation, we get

$z = 10,000,000 + x\\x + y = 10,000,000 + x\\\\\text{Subtracting x from both the sides}\\\\y = 10,000,000$

Thus, Latin music earned y = $10 million from digital sale.

Putting z in place of x + y (as both are equal as stated in first equation) in the third equation,

$x + y + z = 21,000,000\\z + z = 21,000,000\\2z = 21,000,000\\\\\text{Dividing by 2 on both the sides}\\\\z = 10,500,000$

Thus, pop/rock music earned $10,500,000 from digital sale.

Putting this value in second equation, we get

$z = 10,000,000 + x\\10,500,000 = 10,000,000 + x\\500,000 = x$

Thus, tropical music earned $500,000 from its digital sale.

Thus,

The revenue earned by each of the three categories is

• Pop/rock: $10,500,000
• Tropical: $500,000
• Latin: $10,000,000

Learn more about system of equations here:

https://brainly.com/question/13722693