SOLUTION: Tickets to a local movie were sold for $6.00 for adults and $4.50 for students. If 276 tickets were sold for a total of $1632.00, how many student tickets were sold?

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Question 1208613: Tickets to a local movie were sold for $6.00 for adults and $4.50 for students. If 276 tickets were sold for a total of $1632.00, how many student tickets were sold?
Found 3 solutions by math_tutor2020, josgarithmetic, greenestamps:
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

x = number of adults
y = number of students

x+y = 276 since there are 276 total people
Solving for x gives us x = -y+276

6x = money from just the adults
4.5y = money from just the students

6x+4.5y = total amount of money brought in
6x+4.5y = 1632
6( x )+4.5y = 1632
6( -y+276 )+4.5y = 1632 ....... replace x with -y+276
I'll let the student take over from here.

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
adult price $6
student price $4.5
If a adults then 276-a students;
Revenue $1632

6a%2B4.5%28276-a%29=1632
-
6a-4.5a%2B%284.5%29%28276%29=1632
1.5a=1632-%284.5%29%28276%29
highlight_green%28a=%281632-%284.5%29%28276%29%29%2F1.5%29
and you can finish..

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


x = # of adult tickets
y = # of student tickets

The given information gives us these two equations:

x%2By=276 the total number of tickets sold was 276

6x%2B4.50y=1632 the total cost of the tickets, at $6 each for adults and $4.50 each for students, was $1632

In both of the responses you have received from other tutors, the solution of the problem is set up using substitution -- solving the first equation for either x or y and substituting in the second.

When both equations are given in this "ax+by=c" form, I think a solution using elimination is easier.

Multiply the first equation by 6 so that both equations contain the term "6x":

6x%2B6y=1656
6x%2B4.5y=1632

Now subtract the second equation from the first, eliminating variable x, and solve the resulting equation for y:

1.5y=24
y=24%2F1.5=16

The number of student tickets sold was y = 16.

ANSWER: 16

CHECK:
The number of student tickets was 16, so the number of adult tickets was 276-16 = 260.
260(6)+16(4.5)=1560+72=1632