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 $23 million. Tropical music brought in twice as much as urban music, and pop/rock music brought in $11 million more than the others combined. How much revenue was earned from digital sales in each of the three categories?

1. pop/rock music $
2. tropical music$
3. urban Latin music $

Answer 1

Pop/rock = 17 million

Urban Latin= 2 million

Tropical = 4 million

Explanation:

Let the pop/rock be denoted by P

Urban be denoted by U

And T represents tropical.

From the first statement

"total revenues from digital sales of pop/rock, tropical (salsa/merengue/cumbia/bachata), and urban (reggaeton) Latin music in a certain country amounted to $23 "

We can deduct that

P + T +U = 23000000.......eqn(I)

From the second statement

"Tropical music brought in twice as much as urban music"

We can say T = 2U ......eqn(II)

And P-(T+U)=11000000

P- T-U= 11000000...... eqn(III)

Putting equation 2 in both equations we have

P + (2U)+ U = 23000000

P+ 3U = 23000000......eqn iv

Then putting

P - (2U)-U = 23000000

P - 3U= 23000000.......eqn v

Combining eqn Iv and v

P+ 3U = 23000000......eqn iv

P - 3U= 11000000.......eqn v

Solving simultaneously using elimination i.e adding the 2 equations

2P= 34000000

P= 17000000

Substituting P to the first equation

17000000+3U = 23000000

3U = 23000000-17000000

3U = 6000000

U = 2000000

And since T = 2U

T= 2* 2000000

T= 4000000.