Final answer:
The question involves solving a system of equations to determine the number of tickets sold at the door for a dance. By setting up equations for the total tickets and the total revenue, we found that 75 tickets were sold at the door.
Step-by-step explanation:
The question you've asked is a linear algebra problem typically found in high school mathematics. We need to find out how many tickets were sold at the door for the homecoming dance. To solve this, we will use a system of equations.
Let's define two variables, e for the number of early tickets sold at $5 each and d for the number of door tickets sold at $7 each. The equation based on the total number of tickets sold is e + d = 137. The equation based on the total revenue is 5e + 7d = 835. Solving these simultaneous equations will give us the values for e and d.
First, we can multiply the first equation by 5, which gives us 5e + 5d = 685. Now, let's subtract this from the revenue equation:
- 5e + 7d = 835
- -(5e + 5d = 685)
This subtraction yields 2d = 150. Dividing both sides by 2, we get d = 75. Thus, 75 tickets were sold at the door.