Question 1135060: A used computer sells for 20 dollars more than four times the amount of a set of speakers. A used monitor sells for forty dollars less than three times what the speakers sell for. If they sell for 580 dollars all together, how much does each item sell for?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
C = price of computer
S = price of speakers
M = price of monitor
all prices are in dollars
one equation is C = 4*S+20 since "A used computer sells for 20 dollars more than four times the amount of a set of speakers"
another equation is M = 3*S-40 because "A used monitor sells for forty dollars less than three times what the speakers sell for"
Finally, the last equation is C+S+M = 580 because the problem states "they sell for 580 dollars all together"
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Use substitution to solve for S
C+S+M = 580 ... start with the third equation
4S+20+S+M = 580 .... replace C with 4S+20
4S+20+S+3S-40 = 580 .... replace M with 3S-40; note how we have one variable now
8S-20 = 580
8S-20+20 = 580+20 ... add 20 to both sides
8S = 600
8S/8 = 600/8 ... divide both sides by 8
S = 75
The speakers sell for 75 dollars
Use this value of S to find M
M = 3*S-40
M = 3*75-40
M = 225-40
M = 185
The monitor is 185 dollars
Finally, use the value of S to find the value of C
C = 4*S + 20
C = 4*75 + 20
C = 300 + 20
C = 320
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Answers:
Computer = 320 dollars
Speakers = 75 dollars
Monitor = 185 dollars
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