SOLUTION: An auditorium sold 1200 tickets to a recent magic show. Ticket prices were $5 for adults and $3 for children. They took in $5180. How many adult tickets and how many children's tic

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Question 94406: An auditorium sold 1200 tickets to a recent magic show. Ticket prices were $5 for adults and $3 for children. They took in $5180. How many adult tickets and how many children's tickets we sold?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = no. of adult ticket sold, and c = no. of children's tickets
:
Write an equation representing each statement:
"An auditorium sold 1200 tickets to a recent magic show."
a + c = 1200
Rearrange equation to be used for substitution (subtract a from both sides):
c = (1200 - a)
:
"Ticket prices were $5 for adults and $3 for children. They took in $5180."
5a + 3c = 5180
:
How many adult tickets and how many children's tickets we sold?
:
Substitute (1200-a) for c in the above equation:
5a + 3(1200-a) = 5180
5a + 3600 - 3a = 5180; multiplied what's inside the bracket
5a - 3a = 5180 - 3600; subtract 3600 from both sides
2a = 1580
a = 1580/2
a = 790 adults
:
You know the total was 1200 so it is an easy matter to find the no. of children
:
Check your solutions in 5a + 3c = 5180 equation
:
Any questions?