Let's solve this problem using a system of equations. Let's assume the number of general admission tickets sold is represented by 'x' and the number of reserved seats sold is represented by 'y'.
We know that the total number of paid admissions is 845, so we can write the equation:
x + y = 845 (Equation 1)
We also know that the total receipts from ticket sales is $4210.50. Since the price for general admission is $4.50 and the price for reserved seats is $6.00, we can write the equation:
4.50x + 6.00y = 4210.50 (Equation 2)
Now, we can solve this system of equations to find the values of 'x' and 'y'.
From Equation 1, we can rewrite it as:
x = 845 - y
Substituting this value of 'x' into Equation 2, we get:
4.50(845 - y) + 6.00y = 4210.50
Expanding and simplifying:
3802.50 - 4.50y + 6.00y = 4210.50
Combine like terms:
1.50y = 408.00
Divide both sides by 1.50:
y = 272
Substituting this value of 'y' back into Equation 1, we can solve for 'x':
x + 272 = 845
x = 573
Therefore, 573 general admission tickets and 272 reserved seats were sold.