To determine the cost of the charity gala for 79 attendees based on a given cost for 58 attendees, we will use the concept of direct proportionality. Direct proportionality means that as one quantity increases, the other quantity increases at the same rate.
Here are the given values:
- The cost of the gala for 58 attendees is [tex]$2,726.
- We need to find the cost of the gala for 79 attendees.
Let's follow these steps:
1. Determine the constant of proportionality:
The cost per attendee can be found by dividing the total cost by the number of attendees. This constant helps us understand the rate at which the cost increases with the number of attendees.
\[
\text{Cost per attendee} = \frac{\text{Total Cost for 58 attendees}}{\text{Number of attendees (58)}}
\]
Substitute the known values:
\[
\text{Cost per attendee} = \frac{2726}{58} = 47
\]
2. Use the constant to calculate the cost for 79 attendees:
Since the cost per attendee is constant, we can now find the total cost for 79 attendees by multiplying this cost per attendee by the number of attendees (79).
\[
\text{Total cost for 79 attendees} = \text{Cost per attendee} \times \text{Number of attendees (79)}
\]
Substitute the constant we found and the number of attendees:
\[
\text{Total cost for 79 attendees} = 47 \times 79 = 3713
\]
So, the cost of the charity gala for 79 attendees will be $[/tex]3,713.
