Final answer:
The total cost for a school banquet with variable attendees can be represented by the linear equation y = 95 + 15x. Substituting x with 77 people, the cost is $1,250, which is calculated using the equation y = 95 + 15 × 77.
Step-by-step explanation:
The cost of a school banquet is represented by a linear equation where the cost is a function of the number of people attending. We need to consider the fixed cost and the variable cost per person to write the equation. The fixed cost is the initial amount that will be charged regardless of the number of people attending, which is $95. The variable cost is the amount that increases with each additional person attending, which is $15 per person.
To represent this mathematically, let x be the number of people attending the banquet, and let y be the total cost. The equation to represent the total cost as a function of the number of people attending is:
y = 95 + 15x
To find the cost for 77 people, we substitute x with 77:
y = 95 + 15 × 77
Now, calculate the total cost:
y = 95 + 1155
y = 1250
Therefore, the cost for 77 people attending the school banquet is $1,250.