A concert venue sold 1425 tickets one evening. Tickets cost $40.00 for a covered pavilion seat and $30.00 for a lawn seat. Total receipts were $48,000.00. How many of each type of ticket were sold?
40p + 30(1425-p) = 48000
To find out how many of each type of ticket were sold, we can set up a system of equations based on the information provided.
Let's assume that the number of covered pavilion seats sold is represented by 'x', and the number of lawn seats sold is represented by 'y'.
From the first piece of information, we know that 1425 tickets were sold in total. So, we can write the equation:
x + y = 1425
From the second piece of information, we know that the total receipts were $48,000.00. The cost of a covered pavilion seat is $40.00, and the cost of a lawn seat is $30.00. So, we can write the equation:
40x + 30y = 48000
Now we have a system of two equations:
x + y = 1425
40x + 30y = 48000
To solve this system, we can use the method of substitution or elimination. For simplicity, let's use the method of substitution.
First, solve the first equation for x in terms of y:
x = 1425 - y
Substitute this value of x into the second equation:
40(1425 - y) + 30y = 48000
Simplify and solve for y:
57000 - 40y + 30y = 48000
10y = 9000
y = 900
Now that we have the value of y, substitute it back into the first equation to find x:
x + 900 = 1425
x = 525
Therefore, 525 covered pavilion seats and 900 lawn seats were sold.