Question

Please answer in detail. I am confused because the two equations are equal to each other. How do I find the number of grills and attendees. My teacher wants exact numbers.

Kyle hosted a massive networking cookout last weekend and wants to write it off as a business expense for his taxes. The problem is, the cookout was so big Kyle can't remember how many people attended or even how many grills he rented. What he does know is that he supplied each grill with 14 burgers and 28 hot dogs, all of which were cooked. He also found 2 burgers and 4 hot dogs left over after the event. If the average cookout attendee ate 1 burger and 2 hot dogs, how many people attended the cookout? How many grills did Kyle rent?

A: Let x be the number of grills Kyle rented. If each grill cooked 28 hot dogs, how can we express the number of hot dogs that were cooked?

  

B: Let y be the number of people who attended the cookout. If each person ate an average of 2 hot dogs, how can we express the number of hot dogs that were eaten?

  

C: Set the number of hot dogs cooked equal to the number eaten plus the number remaining. This will give you a "hot dog" equation.

D: Repeat steps A through C for the burgers to obtain a "burger" equation.

E: Solve the equations to determine both the number of grills and the number of attendees.

Number of grills:   

Number of attendees:   

Answer 1

A: Let x be the number of grills Kyle rented. If each grill cooked 28 hot dogs, how can we express the number of hot dogs that were cooked?
Number of hot dogs that were cooked =	28 x
B: Let y be the number of people who attended the cookout. If each person ate an average of 2 hot dogs, how can we express the number of hot dogs that were eaten?
The total hotdogs eaten = 2y
C: Set the number of hot dogs cooked equal to the number eaten plus the number remaining. This will give you a "hot dog" equation.
Hot dog equation: 28x = 2y + 4
D: Repeat steps A through C for the burgers to obtain a "burger" equation.
Number of burgers cooked = 14x
The total burgers eaten = y
Burger equation: 14x = y+2
E: Solve the equations to determine both the number of grills and the number of attendees.
Both equationsa re the same i.e the hot dog equation (28x-2y=4) reduces to 14x-y=2 by dividing the hot do equation by 2
Thus, there are infinite solutions to the problem. In the table below are a few of those:
Equation: 14 x (Grills) - Attendees = 2 or Attendees =14 x Grills -2
Number of grills:	1	2	3	4	5
Number of attendees:	12	26	40	54	68