MATH SOLVE

4 months ago

Q:
# 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?

Accepted Solution

A:

Answer:Pop/Rock sold $14 millionTropical music sold $3 millionReggaeton sold $4 million.Step-by-step explanation:First let's write the music genre as follows:X = Pop/RockY = TropicalZ = Reggaeton[tex]\left \bigg \{ {{X + Y + Z = 21 (1) } \atop {X=2(Y + Z) (2)}} \text{; } Β \left \bigg \{ {{X + Y + Z = 21 (1)} \atop {X= Z + 10 Β (3)}[/tex]Let's use [tex](2)[/tex] in [tex](1)[/tex]:[tex]X + Y + Z = 21 \Rightarrow 2(Y + Z) + Y + Z = 21 \Rightarrow\\3(Y+Z) = 21 \Rightarrow Y+Z = 7[/tex]Then,[tex]X + 7 = 21 \Righarrow X = 14[/tex]Now let's solve for Z,[tex]14 = Z +10 \Rightarrow Z = 4[/tex]Finally, let's solve for Y,[tex]14 = 2(Y + 4) \Rightarrow Y + 4 = 7 \Rightarrow Y = 3[/tex]So Pop/Rock sold $14 million, Tropical music sold $3 million and Reggaeton sold $4 million.