SOLUTION: Salisbury High School decided to take their students on a field trip to a theme park. A total of 150 people went on the trip. Adults pay $45.00 for a ticket and students pay $28.50

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Question 428235: Salisbury High School decided to take their students on a field trip to a theme park. A total of 150 people went on the trip. Adults pay $45.00 for a ticket and students pay $28.50 for a ticket. How many students and how many adults went to the park if they paid a total of $4770?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+s+= number of students on trip
+a+ = number of adults on trip
given:
(1) +s+%2B+a+=+150+
(2) 4500a+%2B+2850s+=+477000+ (in cents)
----------------
Multiply both sides of (1) by 2850
and subtract (1) from (2)
(2) 4500a+%2B+2850s+=+477000+
(1) -2850a+-+2850s+=+-427500+
+1650a+=+49500+
+a+=+30+
and, since
(1) +s+%2B+a+=+150+
(1) +s+%2B+30+=+150+
+s+=+120+
There were 30 adults and 120 students
check:
(2) 4500a+%2B+2850s+=+477000+
(2) 4500%2A30+%2B+2850%2A120+=+477000+
+135000+%2B+342000+=+477000+
+477000+=+477000+
OK