Final answer:
2,682 day passes and 2,269 weekend passes were sold.
Step-by-step explanation:
Let's denote the number of day passes sold as x and the number of weekend passes sold as y. According to the given information, the cost of a day pass is $81 and the cost of a weekend pass is $120. The total ticket sales for the festival were $489,321.
From the given information, we can set up the following equations:
x = y + 413 (1) (There were 413 more day passes sold than weekend passes)
81x + 120y = 489,321 (2) (The total ticket sales for the festival)
Now we can solve these equations to find the values of x and y.
Substituting the value of x from equation (1) into equation (2):
81(y + 413) + 120y = 489,321
81y + 33,453 + 120y = 489,321
201y = 455,868
y = 2,269
Substituting the value of y into equation (1):
x = 2,269 + 413
x = 2,682
Therefore, 2,682 day passes and 2,269 weekend passes were sold.