One evening 1500 concert tickets were sold for the Fairmont summer jazz festival. Tickets cost $25 for covered pavilion seats and $20 for lawn seats. Total receipts were $35,000.How many of each type of tickets were sold?
P = L + 5
25P + 20L = 35000
Substitute L+5 for P in second equation and solve for L. Then solve for P.
Find the slope of the line containing the given pair of points. If the slope is undefined, state this.
(−4,6) and (2,1)
To determine the number of covered pavilion seats and lawn seats sold, we can use a system of equations.
Let's denote the number of covered pavilion seats as "x" and the number of lawn seats as "y".
From the problem, we have two important pieces of information:
1. The total number of tickets sold is 1500:
x + y = 1500
2. The total revenue from ticket sales is $35,000:
25x + 20y = 35000
We can now solve this system of equations to find the values of x and y.
One way to solve this system is by using substitution:
1. Solve the first equation for x:
x = 1500 - y
2. Substitute this value of x into the second equation:
25(1500 - y) + 20y = 35000
Now, solve this equation to find the value of y:
37500 - 25y + 20y = 35000
-5y = -2500
y = 500
Now that we found the value of y, substitute it back into the first equation to find x:
x + 500 = 1500
x = 1000
Therefore, 1000 covered pavilion seats and 500 lawn seats were sold at the Fairmont summer jazz festival.