Question

The 9th graders are selling tickets to raise money for a class field trip. They are selling student tickets for $5 and adult tickets for $9. The 9th graders received a total of $240 from sales. In total, 40 tickets were sold. Write a system to represent this situation. Be sure to define your variables. Use your system to determine how many tickets of each type the students sold.

Answer 1

Total number of adult tickets sold = 10

Total Number of Students tickets sold = 30

Explanation:

Let
`x` be the number of student tickets sold.

Let
`y` be the number of adult tickets sold.

As per the question statement, total tickets sold are 40.

`x +y =40 ...... (1)`

Price of each student ticket = $5

Sales from students' tickets = Price of each students ticket
`*` Number of students tickets sold

Sales from student's tickets = 5
`* x`

Price of each adult ticket = $9

Sales from adult's tickets = Price of each adult's ticket
`*` Number of adult tickets sold

Sales from student's tickets = 9
`* y`

Total sales is done by students and adult tickets is $240 as per the question statement.

`\Rightarrow 5x + 9y = 240 ......(2)`

Solving equations (1) and (2) using elimination method:

Equation
`(2) - 5 * (1)` :

`5x + 9y -5x-5y = 240-200\\\Rightarrow 4y = 40\\\Rightarrow y =10`

Total number of adult tickets sold = 10

Putting
`y=10` in equation (1):

`x+10 = 40\\\Rightarrow x = 30`

Total number of students tickets sold = 30

Total number of adult tickets sold = 10

Total Number of Students tickets sold = 30