Question

Football game admission is $2.00 for general admission and $6.50 for reserved seats . The receipts were $3953.00 for 1297 paid admissions .How many of each ticket were sold? (round to the nearest intergar if necessary .) ___ general admission tickets sold .____reserved seating tickets sold.

Answer 1

Let x represent the number of general admission tickets sold.

Let y represent the number of reserved seating tickets sold.

We were told that general admission ticket costs $2 each and reserved seating ticket costs $6.50 each. This means that the cost of x general admission tickets and y reserved seating tickets would be

2x + 6.5y

The total amount received was $3953. It means that

2x + 6.5y = 3953

Also, the total number of tickets sold was 1297. It means that

x + y = 1297

x = 1297 - y

Substituting x = 1297 - y into 2x + 6.5y = 3953, it becomes

2(1297 - y) + 6.5y = 3953

2594 - 2y + 6.5y = 3953

- 2y + 6.5y = 3953 - 2594

4.5y = 1360

y = 1360/4.5

y = 302.22

Rounding to the nearest integer,

y = 302

x = 1297 - y = 1297 - 302

x = 995

995 general admission tickets were sold .

302 reserved seating tickets were sold