Question

a music festival sold two types of tickets, day passes and weekend passes. the day passes were $81, and the weekend pass was $120. the total ticket sales for the festival were $489,321. they sold 413 more day passes than weekend passes. how many day passes and how many weekend passes were sold?

Answer 1

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.