SOLUTION: 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

Algebra ->  Matrices-and-determiminant -> SOLUTION: 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      Log On


   

Question 1111370: 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 $8 million more than tropical music. How much revenue was earned from digital sales in each of the three categories?
pop/rock music $
million
tropical music $
million
urban Latin music $
million
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
p, pop/rock
t, tropical
u, urban-reggaeton

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total revenue,... amounted to $21 million. Pop/rock music brought in twice as much as the other two categories combined and $8 million more than tropical music.
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The description and assigned variables give this system of equations:
system%28p%2Bt%2Bu=21%2Cp=2%28t%2Bu%29%2Cp=t%2B8%29


Substitute for p, and simplify:
system%282t%2Bu=13%2Ct%2B2u=8%29
.
.
system%28u=1%2Ct=6%2Cp=14%29

14 million, pop/rock
6 million, tropical
1 million, urban

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The formal algebraic solution is good exercise in using algebra.

The problem can also provide good mental exercise if you solve it by logical reasoning and a bit of basic arithmetic.

Pop/rock brought in twice as much as the others together; that means pop/rock was 2/3 of the total.

2/3 of the total $21 million is $14 million, leaving $7 million for the other two categories.

The $14 million for pop/rock was $8 million more than for tropical music, so tropical music brought in $6 million.

That leaves $1 million for urban music.

Answer: pop/rock $14 million; tropical $6 million; urban $1 million.