Question

In 2013, total revenues from digital sales of regional (Mexican/Tejano), pop/rock, and tropical (salsa/merengue/cumbia/bachata) Latin music in the United States amounted to to $58 million. Regional music brought in four times as much as much as tropical music and pop/rock music brought in $10 million more than tropical music. How much revenue was earned from digital sales in each of the three categories

Answer 1

Answer:

Regional = 32 million

Pop/rock = 18 million

Tropical = 8 million

Explanation:

Given that

Total sales of the 3 categories = 58 million.

Let a denote regional

b denote pop/rock

c denote tropical

Thus

a + b + c = 58 million

From the question

a = 4c (regional 4 times tropical). equation 2.

Also, pop/rock music brought in $10 million more than tropical music

Thus,

b = c + 10. equation 3.

By eliminating a and b, put equation 2 and 3 in 1

We have

a + b + c = 58

4c + c + 10 + c = 58.

Collect like terms,

6c = 58 - 10

c = 48 ÷ 6

c = 8

Thus, tropical music = 8 million.

Recall that,

a = 4c

Thus

a = 4 × 8

= 32.

Therefore regional music = 32 million.

Again, recall that,

b = c + 10

Thus, b = 8 + 10

= 18

Therefore, pop/rock = 18 million.

8 + 18 + 32 = 58

Answer 2

Answer: Tropical Music sales  = $ 8000 000

Explanation:

Total digital sales = $58000 000

Regional Music sales = 4 x tropical Music sales

Pop/rock music sales = Tropical Music sales + 10 000 000

Let Tropical Music sales be y

Total sales = Regional sales + Tropical sales + Pop/rock sales

58000 000 = 4y + y + (y+10000000)

58000 000 = 6y + 10000000

6y = 58000 000 - 10000000

y =  48000 000/6 = 8000 000

Tropical Music sales  = $ 8000 000