Question

Searches related to A 500-seat theater charges $5 per ticket for students and $8 per ticket for adults. All seats for the performance tonight are filled and total ticket sales are $3400. Which two equations below form a system of equations that you could use to determine how many student tickets and how many adult tickets were sold if x = the number of student tickets sold and y = the number of adult tickets sold?

Answer 1

Number of tickets sold to students and adults are 200 and 300 respectively.

Explanation:

Let, the number of student tickets = x and number of adult tickets = y.

As, there are total number of 500 seats in the theater, we have,

`x+y=500`

Also, the price of the tickets is $5 per student and $8 per adult.

Since, the total sales are of $3400. We get,

`5x+8y=3400`

So, the system of equations is given by,

x+y=500 ........................... (1)

5x+8y=3400 ..........................(2)

Multiply equation (1) by 5 and subtract with equation (2), we get,

3y = 900 i.e. y= 300

So, x=500-y implies x=500-300 i.e. x= 200

Hence, the number of tickets sold to students and adults are 200 and 300 respectively.

Answer 2

The system of equation form is
`x+y=500` and
`5x+8y=3400`

Student tickets sold is 200 and Adult tickets sold is 300.

Explanation:

Given : Searches related to A 500-seat theater charges $5 per ticket for students and $8 per ticket for adults. All seats for the performance tonight are filled and total ticket sales are $3400.

To find : The system of equation form to determine how many student tickets and how many adult tickets were sold.

Solution :

Let x = the number of student tickets sold.

Let y = the number of adult tickets sold.

A 500-seat theater charges $5 per ticket for students and $8 per ticket for adults. Total ticket sales are $3400.

`x+y=500` ........[1]

`5x+8y=3400` .......[2]

The system of equation form is
`x+y=500` and
`5x+8y=3400`

Now, we solve the system of equations

Substitute x=500-y from [1] in [2]

`5x+8y=3400`

`5(500-y)+8y=3400`

`2500-5y+8y=3400`

`3y=900`

`y=300`

Put back in equation [1]

`x+300=500`

`x=200`

Therefore, Student tickets sold is 200 and Adult tickets sold is 300.