Question

Admission to a baseball game is $4.00 for general admission and $4.50 for reserved seats. The receipts were $5150.00 for 1255 paid admission. How many of each ticket were sold?

Answer 1

995 general admission tickets and 260 reserved seat tickets

Explanation:

We can solve this by using Simultaneous equations.

General admission is $4.00 and each Reserved seat is $4.50.

Let g represent the number of General admission tickets and r represent the number of Reserved seat tickets.

The total amount paid for 1255 tickets is $5150.00.

This means two things:

1. The total number of tickets is 1255, which means if we add the general admission tickets and the number of reserved seat tickets, we will get 1255:

g + r = 1255 ________________ (1)

2. The total price of all tickets is $5150.00, which means if we multiply the number of general admission tickets by the price of general admission tickets and we multiply the number of reserved seat tickets by the price of reserved seat tickets and add them up, we will get $5150:

(4.00*g) + (4.50*r) = 5150 _________(2)

=> g + r = 1255 __________________(1)

(4.00*g) + (4.50*r) = 5150 _________(2)

From (1):

g = 1255 - r _______ (3)

Putting (3) in (2):

{4.00*(1255 - r)} + (4.50*r) = 5150

5020 - 4.00r + 4.50r = 5150

5020 + 0.50r = 5150

=> 0.50r = 5150 - 5020

0.50r = 130

r = 130 / 0.50 = 260

Putting the value of r in (3):

g = 1255 - 260 = 995

Hence, 995 general admission tickets and 260 reserved seat tickets were sold.