A total of 800 tickets for the covered pavilion and 700 tickets for lawn seats were sold, solved using a system of equations.
We assume the number of covered pavilion tickets sold to be x and the number of lawn seat tickets sold to be y.
As a total of 1500 tickets were sold, we can form an equation:
x + y = 1500 ... (i),
as we had only those two types of tickets.
The cost of each covered pavilion ticket = $20.
Hence, the total revenue from covered pavilion tickets = $20x.
The cost of each lawn seat ticket = $10.
Hence, the total revenue from lawn seat tickets = $10y.
The total receipts were said to be $23,000.
Thus, we can represent this as an equation:
20x + 10y = 23000 ...(ii).
Combining (i) and (ii), we get a system of equations:
x + y = 1500 ... (i).
20x + 10y = 23000 ... (ii).
Dividing equation (ii) by 10, we get:
2x + y = 2300 ... (iii).
Subtracting (i) from (iii), we get:
2x + y = 2300.
x + y = 1500.
(-) (-) (-)
____________
x = 800.
Substituting x = 800 in (i), we get:
x + y = 1500,
or, 800 + y = 1500,
or, y = 1500 - 800,
or, y = 700.
Thus, a total of 800 tickets for the covered pavilion and 700 tickets for lawn seats were sold, solved using a system of equations.
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