SOLUTION: A movie theater charges $7 for an adult and $4 for a child's ticket. One night, 900 tickets were sold for a total of $5100. How many children attended the movie that night? How

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A movie theater charges $7 for an adult and $4 for a child's ticket. One night, 900 tickets were sold for a total of $5100. How many children attended the movie that night? How       Log On


   

Question 718767: A movie theater charges $7 for an adult and $4 for a child's ticket. One night, 900 tickets were sold for a total of $5100. How many children attended the movie that night? How many adults attended the movie that night?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of adults who attended
Let +c+ = number of children who attended
given:
(1) +a+%2B+c+=+900+
(2) +7a+%2B+4c+=+5100+
---------------------
Multiply both sides of (1) by +4+
and subtract (1) from (2)
(2) +7a+%2B+4c+=+5100+
(1) +-4a+-+4c+=+-3600+
+3a+=+1500+
+a+=+500+
and, since
(1) +500+%2B+c+=+900+
(1) +c+=+400+
500 adults attended
check:
(2) +7a+%2B+4c+=+5100+
(2) +7%2A500+%2B+4%2A400+=+5100+
(2) +3500+%2B+1600+=+5100+
(2) +5100+=+5100+
OK