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 $31

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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 $31      Log On


   

Question 978510: 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 $31 million. Tropical music brought in twice as much as urban music, and pop/rock music brought in $7 million more than the others combined. How much revenue was earned from digital sales in each of the three categories?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = revenue from tropical
Let +p+ = revenue from pop/rock
Let +u+ = revenue fom urban
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Given ( in millions ):
(1) +t+%2B+p+%2B+u+=+31+
(2) +t+=+2u+
(3) +p+=+t+%2B+u+%2B+7+
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This is 3 equations and 3 unknowns,
so I can solve
Substitute (3) into (1)
(1) +t+%2B+p+%2B+u+=+31+
(1) +t+%2B+t+%2B+u+%2B+7+%2B+u+=+31+
(1) +2t+%2B+2u+=+24+
(1) +t+%2B+u+=+12+
Substitute (2) into (1)
(1) +2u+%2B+u+=+12+
(1) +3u+=+12+
(1) +u+=+4+
and
(2) +t+=+2u+
(2) +t+=+2%2A4+
(2) +t+=+8+
and
(3) +p+=+t+%2B+u+%2B+7+
(3) +p+=+8+%2B+4+%2B+7+
(3) +p+=+19+
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Revenue earned was:
$8 million from tropical
$19 million from pop
$4 million from urban
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check:
+8+%2B+19+%2B+4+=+31+
$31 million total revenue
OK