. A drama club was performed in an auditorium that has a capacity of 540. Students had to pay $7 a ticket and adults were charged $10. On opening night, the auditorium was full and they brought in $4764 in ticket sales. Write a system of equations to model this situation and solve it using elimination to find the number of students and the number of adults that attended on opening night.

Question

. A drama club was performed in an auditorium that has a capacity of 540. Students had to pay $7 a ticket and adults were charged $10. On opening night, the auditorium was full and they brought in $4764 in ticket sales. Write a system of equations to model this situation and solve it using elimination to find the number of students and the number of adults that attended on opening night.

Answer 1

adult tickets sold --- x

student tickets sold --- 540-x

solve:
10x + 7(540-x) = 4765

or

x+y = 540
10x + 7y = 4765

Answer 2

Let's denote the number of student tickets sold as "s" and the number of adult tickets sold as "a".

Based on the given information, we can set up the following system of equations:

Equation 1: The total number of tickets sold equals the capacity of the auditorium:
s + a = 540

Equation 2: The total amount of money collected from ticket sales equals $4764:
7s + 10a = 4764

Now we can solve the system of equations using elimination:

Multiply Equation 1 by 7 to match the coefficients of "s":
7s + 7a = 3780 (Equation 1)
7s + 10a = 4764 (Equation 2)

Subtract Equation 1 from Equation 2 to eliminate "s":
(7s + 10a) - (7s + 7a) = 4764 - 3780
7a - 7a + 10a = 984
10a = 984

Divide both sides of the equation by 10:
a = 984/10
a = 98

Now substitute the value of "a" into Equation 1 to find the value of "s":
s + 98 = 540
s = 540 - 98
s = 442

Therefore, there were 442 students and 98 adults that attended on opening night.

Answer 3

To solve this problem, we can define two variables:

Let's say S represents the number of students attending and A represents the number of adults attending on opening night.

Now, let's create a system of equations based on the given information:

Equation 1: The total number of people attending the drama club is the sum of students and adults:
S + A = 540

Equation 2: The total revenue from ticket sales is calculated as follows:
7S + 10A = 4764

To solve this system of equations using elimination, we can multiply Equation 1 by 7 to make the coefficients of S in both equations equal:

7(S + A) = 7(540)
7S + 7A = 3780 [Equation 3]

Now, we can subtract Equation 3 from Equation 2 to eliminate the S term:

(7S + 10A) - (7S + 7A) = 4764 - 3780
3A = 984

To find the value of A, we divide both sides of the equation by 3:

3A/3 = 984/3
A = 328

Now we substitute the value of A back into Equation 1 to find the value of S:

S + 328 = 540
S = 540 - 328
S = 212

Therefore, 212 students and 328 adults attended the drama club on opening night.