Final answer:
By forming a system of equations, we determine the cost of one adult ticket is $11.50 and one children's ticket cost is $9.00. However, these results do not match the provided answer choices, suggesting an issue with the question or answer options.
"The correct option is approximately option B"
Step-by-step explanation:
The student's question is a problem dealing with a system of linear equations. By setting up the relationships described in the problem, we can solve for the cost of an adult ticket and a children's ticket at the movies.
Let A represent the cost of an adult ticket and C represent the cost of a children's ticket. We can write out two equations based on the information provided:
3A + C = $43.50 (Mr. Johnson's Purchase)
2A + 2C = $41.00 (Mrs. Thomas's Purchase)
Now, we can solve this system of equations to find the values of A and C. Let's multiply the second equation by 0.5 to make it easier to eliminate the variable C.
Equation 2 becomes: A + C = $20.50
If we subtract this from the first equation, we get:
2A = $43.50 - $20.50
2A = $23.00
Dividing both sides by 2, we get:
A = $11.50
Now we have the cost of an adult ticket. We can substitute A in either equation to solve for C:
3(11.50) + C = $43.50
34.50 + C = $43.50
Subtracting 34.50 from both sides we get:
C = $43.50 - $34.50
C = $9.00
So the cost of an adult ticket is $11.50 and a children's ticket costs $9.00. However, these values do not match any of the given options, indicating a possible mistake in the question or the options provided.