Question

Tickets for the school play cost $3 for students and $6 for adults. The drama club hopes to bring in at least $450 in sales, and the auditorium has 120 seats. Let a represent the number of adult tickets, and let s represent the number of student tickets.

Answer 1

6A + 3s= 450
A+s=120
S=120-a
6A+3(120-a) =450
6a+360-3a=450
3a=450-360
3a=90
A=30
S=120-30
S=90
Hope this helps

Answer 2

To gain $450, they need to sell 90 student's tickets and 30 adult's tickets.

Explanation:

Givens:

• Student's tickets cost $3.
• Adult's tickets cost $6.
• They wanna make $450.
• The auditorium has 120 seats.

Now,
`a` represents adults and
`s` represents students.

Using these variables and all costs given, we have the following expressions:

`3s+6a=450`; this expresses the total earning they want to make.

`s+a=120`; this shows the capacity of the auditorium, it's distributed between adults and students, which are the two types of tickets.

Now, we have to solve this system of equations to find the value of each variable.

Observe, if we multiply the second equation by -6, we could eliminate one variable and find the other one's value:

`\left \{ {{3s+6a=450} \atop {(s+a=120)(-6)}} \right.\\\\\left \{ {{3s+6a=450} \atop {-6s-6a=-720}} \right.\\ -3s=-270\\s=(-270)/(-3)=90`

Then, we replace this value to find the other one:

`s+a=120\\90+a=120\\a=120-90=30`

Therefore, to gain $450, they need to sell 90 student's tickets and 30 adult's tickets.