Suppose a movie theater sold 200 adult and student tickets for a showing with the revenue of $980. If the adult tickets are $5.50 and the students tickets are $4, how many of each type of ticket were sold?
5.5a + 4(200-a) = 980
solve for a to get # adults tickets
subtract that from 200 to get # child tickets
last friday, a movie theatre sold adult and student tickets to a showing. they sold a total of 200 tickets. The theatre sold 28 more adult tickets than student tickets. The manager wants to know how many adult and how many student tickets were sold?
Let's solve this problem step-by-step:
Let's assume the number of adult tickets sold is "x".
Therefore, the number of student tickets sold can be expressed as "200 - x".
The revenue from the adult tickets can be calculated by multiplying the number of adult tickets by the price per ticket: 5.50 * x = 5.50x.
Similarly, the revenue from the student tickets can be calculated by multiplying the number of student tickets by the price per ticket: 4 * (200 - x) = 800 - 4x.
Given that the total revenue is $980, we can set up the following equation:
5.50x + 800 - 4x = 980.
Now, let's solve this equation for x:
1.5x + 800 = 980.
1.5x = 180.
x = 120.
Therefore, 120 adult tickets were sold.
And the number of student tickets sold is 200 - 120 = 80.
So, 120 adult tickets and 80 student tickets were sold.
To find out the number of adult and student tickets sold, we can set up a system of equations. Let's represent the number of adult tickets as 'a' and the number of student tickets as 's'.
Now, we know that the theater sold a total of 200 tickets, so we can write the first equation as:
a + s = 200
The second equation can be written using the total revenue. The revenue from adult tickets can be calculated by multiplying the number of adult tickets with the price of each adult ticket ($5.50). Similarly, the revenue from student tickets can be calculated by multiplying the number of student tickets with the price of each student ticket ($4). Therefore, the equation is:
5.50a + 4s = 980
Now we have a system of equations:
a + s = 200
5.50a + 4s = 980
We can solve this system using different methods, such as substitution or elimination. Let's solve it using the elimination method, where we multiply the first equation by 4 to eliminate the 's' variable:
4a + 4s = 800
5.50a + 4s = 980
Now, subtract the first equation from the second equation:
5.50a + 4s - (4a + 4s) = 980 - 800
1.50a = 180
Divide both sides by 1.50:
a = 120
Now, substitute the value of 'a' back into the first equation:
120 + s = 200
Subtract 120 from both sides to isolate 's':
s = 80
Therefore, the movie theater sold 120 adult tickets and 80 student tickets.