Question

question 3: the local theater is showing a matinee and offering a special deal for the community. a ticket for an adult costs $11 and a ticket for a child costs $6. the theater sells a total of 60 tickets and collects $460. how many adult tickets x and children tickets y are sold?
system:
x + y = 60

define your variables:
x = ticket price for an adult
y = ticket cost for a child

solution:

Explanation:

Step1: Set up the equations

Let \(x\) = number of adult tickets, \(y\) = number of children tickets.
Total tickets: \(x + y = 60\)
Total revenue: \(11x + 6y = 450\)

Step2: Solve the system

From \(x + y = 60\), get \(y = 60 - x\). Substitute into revenue equation:
\(11x + 6(60 - x) = 450\)
\(11x + 360 - 6x = 450\)
\(5x = 90\)
\(x = 18\)? Wait correction: Wait original system in image says \(x - y = 60\)? No recheck: Wait image shows system \(x - y = 60\)? No original problem says total tickets 60 so \(x + y =60\), revenue 11x+6y=450. Correct calculation:
\(11x +6(60-x)=450\) → \(5x=450-360=90\) → \(x=18\), \(y=42\)? Wait no image system is written as \(x - y=60\) but problem says total tickets 60. Assuming image system is typo: if system is \(x + y=60\) and \(11x+6y=450\), solution is x=18, y=42. If system is \(x - y=60\) (unlikely), no positive y. So correct solution with total tickets 60: 18 adult, 42 children. Wait but let's follow image system: if system is \(x - y=60\) and \(11x+6y=450\), solving: \(x=y+60\), substitute: 11(y+60)+6y=450 →17y=450-660=-210→invalid. So original problem's correct system is \(x+y=60\), so answer x=18, y=42.

Wait correction: Let's redo properly:

Step1: Correct system

\(x + y = 60\) (total tickets)
\(11x + 6y = 450\) (total revenue)

Step2: Substitute \(y=60-x\)

\(11x +6(60-x)=450\)
\(5x=90\) → \(x=18\)

Step3: Find y

\(y=60-18=42\)

Final Answer:

18 adult tickets and 42 children tickets are sold.

Answer:

30 adult tickets and 30 children tickets are sold.