Final answer:
The number of regular admission tickets sold was 64 and the number of student tickets sold was 43.
Step-by-step explanation:
To solve this problem, we need to set up a system of equations based on the given information. Let's denote the number of regular admission tickets sold as 'x' and the number of student tickets sold as 'y'.
From the problem, we know that the total receipts for the showing were $922 and that there were a total of 107 people in the audience. We can set up two equations:
x + y = 107 (equation 1)
9.50x + 7.25y = 922 (equation 2)
We can solve this system of equations using substitution or elimination. Let's use elimination:
Multiply equation 1 by 7.25 to make the coefficients of 'y' the same:
7.25x + 7.25y = 777.75 (equation 3)
Subtract equation 3 from equation 2 to eliminate 'y':
9.50x + 7.25y - 7.25x - 7.25y = 922 - 777.75
2.25x = 144.25
Divide both sides by 2.25 to solve for 'x':
x = 144.25 / 2.25
x = 64
Substitute the value of 'x' back into equation 1 to find 'y':
64 + y = 107
y = 107 - 64
y = 43
Therefore, 64 regular admission tickets were sold and 43 student tickets were sold.