Question

10. Ford Arena has sold a total of 200 tickets for an upcoming concert. Floor seats are $36 and stadium seats are $28. They have sold $6080 in tickets. How many floor seats and how many stadium seats have been sold.

Answer 1

The Ford Arena sold 60 floor seats and 140 stadium seats. We derived this by setting up a system of equations using the total tickets sold and the total revenue, and then solving for the number of each type of seat sold.

Step-by-step explanation:

To determine how many floor seats and stadium seats have been sold at the Ford Arena, we can set up a system of linear equations based on the given information: 200 total tickets sold, with floor seats priced at $36 and stadium seats priced at $28. Further, the total revenue from ticket sales is $6080.

Let's denote the number of floor seats sold as F and the number of stadium seats sold as S. We have two equations to work with:

1. F + S = 200 (the total tickets sold)
2. 36F + 28S = 6080 (the total revenue)

If we multiply the first equation by 28 (the price of stadium seats), we get:

28F + 28S = 5600

Now, by subtracting this from the second equation, we can find the value of F:

(36F + 28S) - (28F + 28S) = 6080 - 5600

8F = 480

F = 60

We can then substitute F back into the first equation to find S:

60 + S = 200

S = 200 - 60

S = 140

Therefore, 60 floor seats and 140 stadium seats have been sold.