Admission to a baseball game is $4.50 for general admission and $5.50 for reserved seats. The receipts were $4588.00 for 948 paid admissions. How many of each ticket were sold?
If the number of general admissions is x, then the rest (948-x) were reserved. So, add up the receipts:
4.50x + 5.50(948-x) = 4588.00
To find the number of general admission and reserved seats sold, we can set up a system of equations.
Let's assume:
- x = number of general admission tickets sold
- y = number of reserved seats sold
From the given information, we know:
- Admission to a baseball game is $4.50 for general admission, so the total revenue from general admission tickets is 4.50x.
- Admission to a baseball game is $5.50 for reserved seats, so the total revenue from reserved seats is 5.50y.
- The total receipts from 948 paid admissions is $4588.00, so we can create an equation: 4.50x + 5.50y = 4588.00.
Now we can solve the system of equations:
Equation 1: 4.50x + 5.50y = 4588.00
Equation 2: x + y = 948
To solve this system, we can use the substitution method or the elimination method. Let's use the elimination method.
Multiply Equation 2 by -4.50 to match the coefficients of x:
-4.50x - 4.50y = -4266.00
Now, add this equation to Equation 1 to eliminate x:
(4.50x + 5.50y) + (-4.50x - 4.50y) = 4588.00 + (-4266.00)
y = 322.00
Now that we have the value of y, we can substitute it back into Equation 2 to find x:
x + 322 = 948
x = 948 - 322
x = 626
Therefore, there were 626 general admission tickets sold and 322 reserved seats sold.