story problem help

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 $26 million. Tropical music brought in twice as much as urban music, and pop/rock music brought in $8 million more than the others combined. How much revenue was earned from digital sales in each of the three categories?

Answer 1

You can write a system of equations for this problem. Let x = pop/rock music profits, y = tropical music profits, and z = urban music profits, each in millions. Then:

 

x + y + z = 26

y = 2z

x = y + z + 8

 

Plug the third equation into the first equation:

 

x + y + z = 26

y + z + 8 + y + z = 26

2y + 2z + 8 = 26

2y + 2z = 18

 

Plug the second equation into this new equation:

 

2y + 2z = 18

2(2z) + 2z = 18

4z + 2z = 18

6z = 18

z = 3

 

Now, plug that back into the second equation to find y:

 

y = 2z

y = 2(3)

y = 6

 

Finally, plug both values into the third equation:

 

x = y + z + 8

x = 6 + 3 + 8

x = 17

 

So, pop/rock music made $17 million, tropical music made $6 million, and urban music made $3 million.