Question

A restaurant charges $100 to rent its banquet room for an event. It also charges $15 to serve dinner to each guest. Write an equation for the total cost (t) of renting the banquet room in terms of the number of guests (g). How many guests attend if the total cost of an event is $2200? Btw I need two answers because its asking for the equation and the amount of guests

A. Equation: t = 15g + 100, Guests: 120
B. Equation: t = 100g + 15, Guests: 120
C. Equation: t = 15g + 100, Guests: 140
D. Equation: t = 100g + 15, Guests: 140

Answer 1

The total cost of renting the banquet room is represented by the equation t = 15g + 100. To find the number of guests when the total cost is $2200, we substitute and solve the equation to get 140 guests.

Step-by-step explanation:

To determine the equation for the total cost (t) of renting the banquet room in terms of the number of guests (g), we have to consider both the fixed cost for the room and the variable cost per guest. The fixed cost to rent the room is $100, regardless of the number of guests. The variable cost is $15 per guest. Therefore, the total cost is comprised of the fixed cost plus the variable cost multiplied by the number of guests. The equation that represents this relationship is t = 15g + 100.

To find out how many guests attended an event that had a total cost of $2200, we can substitute the total cost into the equation and solve for g:

t = 15g + 100
2200 = 15g + 100
2200 - 100 = 15g
2100 = 15g
g = 2100 / 15
g = 140 guests

Hence, the correct answer is: Equation: t = 15g + 100, Guests: 140.