Question

Admission to a baseball game is $2.50 for general admission and $5.00 for reserved seats. The receipts were $2882.50 for 876 paid admissions. How many of each ticket were sold?

Answer 1

Answer:

599 general admission tickets were sold while 277 reserved seats admission tickets were sold

Step-by-step explanation:

Here, we want to know the number of each types of tickets sold.

Let the number of general admission ticket be x while the number of reserved seats ticket be y

Mathematically since the total of both tickets is 876;

then;

x + y = 876 ••••••••••••(i)

The total amount of money generated from general admission is cost of general admission ticket * the number of general admission tickets sold = $2.50 * x = $2.50x

The total amount of money generated from reserved seat admission tickets sales is cost of reserved seat admission ticket * the number of reserved seats admission ticket sold = $5 * y = $5y

Adding both gives $2882.50

Thus;

2.5x + 5y = 2882.5 •••••••••(ii)

Now, from i, let’s say x = 876 -y

Let’s insert this into ii

2.5(876-y) + 5y = 2882.5

2190 -2.5y + 5y = 2882.5

2190 + 2.5y = 2882.5

2.5y = 2882.5 - 2190

2.5y = 692.5

y = 692.5/2.5

y = 277

Recall;

x = 876 -y

Thus;

x = 876 - 277 = 599