This problem involves solving a system of linear equations.

Step 1: Define variables

Let:

• $x$ = price of an adult ticket
• $y$ = price of a child ticket

Step 2: Form equations from the given information

From the first night: $7x + 11y = 227$

From the second night: $6x + 6y = 150$

Step 3: Solve the system of equations

We now solve this system using substitution or elimination. Let's proceed with elimination:

Step 3.1: Simplify the second equation

Divide the second equation by 3: $2x + 2y = 50$

Step 3.2: Eliminate one variable

Multiply the simplified second equation by 7: $14x + 14y = 350$

Multiply the first equation by 2: $14x + 22y = 454$

Now subtract the second equation from the first: $(14x + 22y) - (14x + 14y) = 454 - 350$ $8y = 104$ $y = 13$

Step 3.3: Solve for $x$

Substitute $y = 13$ into the simplified second equation: $2x + 2(13) = 50$ $2x + 26 = 50$ $2x = 24$ $x = 12$

Final Answer:

• The price of an adult ticket is $12.
• The price of a child ticket is $13.

Would you like me to verify or elaborate further? Here are 5 related questions to extend the understanding:

1. How would you graphically represent this system of equations?
2. How does substitution differ from elimination in solving linear equations?
3. Could this problem be solved using matrices? How?
4. How would the solution change if the ticket prices were integers only?
5. What other real-world situations could this type of problem model?

Tip: When solving systems of equations, double-check arithmetic at each step to ensure no errors are made!