SOLUTION: Tickets to the Valentine Dance cost $3 per person or $5 per couple. If $475 worth of tickets were sold and 180 people attended the dance, how many couples were there?
Question 683020: Tickets to the Valentine Dance cost $3 per person or $5 per couple. If $475 worth of tickets were sold and 180 people attended the dance, how many couples were there? Answer by DrBeeee(684) (Show Source):
You can put this solution on YOUR website! Let p = number of single persons
Let c = number of couples
Then you have two equations, one for amount of sales and one for the number of attendees.
(1) 3p + 5c = 475 and
(2) p + 2c = 180
Solve (2) for p and substitute it into (1) to yield
(3) 3(180 - 2c) +5c = 475 or
(4) 540 - 6c + 5c = 475 or
(5) c = 540 - 475 or
(6) c = 65.
Put (6) into (2) and get
(7) p + 2*65 = 180 or
(8) p = 180 - 130 or
(9) p = 50
Let's use (1) to check the numbers.
Is (3*50 + 5*65 = 475)?
Is (150 + 325 = 475)?
Is (475 = 475)? Yes
Answer: There were 65 couples that attended the Valentine Dance.
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