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?

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


   

Question 588435: 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 josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = number of couples
Let +s+ = number of single persons
given:
(1) +s+%2B+2c+=+180+
(2) +3s+%2B+5c+=+475+
-----------------
Multiply both sides of (1) by 3
and subtract (2) from (1)
(1) +3s+%2B+6c+=+540+
(2) +-3s+-+5c+=+-475+
+c+=+65+
Substitute this into (1)
(1) +s+%2B+2c+=+180+
(1) +s+%2B+2%2A65+=+180+
(1) +s+%2B+130+=+180+
(1) +s+=+50+
There were 65 couples
check:
(2) +3s+%2B+5c+=+475+
(2) +3%2A50+%2B+5%2A65+=+475+
(2) +150+%2B+325+=+475+
(2) +475+=+475+
OK