really struggling with this problem
admission to a baseball game is $2.00 for general admission and $5.50 for reserved seats. The receipts were $3408.00 for 1025 paid admissions. How many of each ticket were sold?
Let G = gen. adm. and R = reserved seats
G + R = 1025
R = 1025 - G
2G + 5.5R = 3408
Substitute 1025 - G for R in the second equation to solve for G. Put that value in the first equation to find R. To check, put both values in the second equation.
To solve this problem, we need to set up a system of equations based on the given information. Let's say 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 1025, so our first equation is:
x + y = 1025
Next, we can use the ticket prices and the total receipts to form a second equation. General admission tickets cost $2.00 each, and reserved seats cost $5.50 each. So the equation for the total receipts can be written as:
2x + 5.50y = 3408.00
Now we have a system of equations that we can solve simultaneously. There are several methods to solve this system, such as substitution or elimination. Let's solve it using the method of substitution.
From the first equation, we have x = 1025 - y. We can substitute this value of x into the second equation:
2(1025 - y) + 5.50y = 3408.00
Simplifying the equation, we get:
2050 - 2y + 5.50y = 3408.00
Combining like terms, we have:
3.50y = 1358.00
Dividing both sides of the equation by 3.50, we find:
y = 388
Now, substitute this value back into x = 1025 - y:
x = 1025 - 388
x = 637
So, 637 general admission tickets and 388 reserved seats were sold.
To summarize:
Number of general admission tickets sold: 637
Number of reserved seats sold: 388