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.