Question

A nonprofit organization is preparing for its annual fundraiser. The quote to reserve a banquet hall for the evening is $6,750, and there is a $50 charge per person to cater dinner. Write a linear function to represent the cost (y)
, of the banquet hall for x people.(1 point)
The function of the total cost of the banquet hall is
.

Answer 1

To write a linear function representing the total cost \( y \) of the banquet hall for \( x \) people, we need to consider both the fixed cost of reserving the hall and the variable cost of catering dinner.

1. **Fixed Cost**: The cost to reserve the banquet hall is $6,750. This is a constant value and does not depend on the number of people.

2. **Variable Cost**: The cost to cater dinner is $50 per person. This means that the total catering cost increases linearly with the number of people.

The total cost \( y \) can thus be expressed as:

\[
y = 6750 + 50x
\]

where:
- \( y \) is the total cost,
- \( 6750 \) is the fixed cost of the banquet hall,
- \( 50x \) is the variable cost based on the number of people \( x \).

So, the function of the total cost of the banquet hall is:

\[
y = 6750 + 50x
\]