P = L + 5
25P + 20L = 35000
Substitute L+5 for P in second equation and solve for L. Then solve for P.
25P + 20L = 35000
Substitute L+5 for P in second equation and solve for L. Then solve for P.
(β4,6) and (2,1)
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.