Question

A local foundation organized a lunch party for all the kids in the community. They ordered a total of 500 hamburger meals. they ordered plain burgers at $1.75 each, cheeseburgers at $2.50 each, and chicken burgers at $3.20 each. they ordered mostly cheeseburgers and 100 fewer chicken burgers than plain burgers. the total order came to $1,172.50.

define the varibles and write a system of equations to represent the situation.

A)
P + C + H = 500
1.75P + 2.50C + 3.20H = 1172.50

B)
P + C + H = 500
1.75P + 2.50C - 3.20H = 1172.50

C)
P - C + H = 500
1.75P + 2.50C + 3.20H = 1172.50

D)
P + C - H = 500
2.50P + 1.75C + 3.20H = 1172.50​

Answer 1

The correct system of equations to represent the ordering of different types of burgers for a community event is Option A, which aligns with the total number of burgers and the total cost. 'P' represents plain burgers, 'C' is cheeseburgers, and 'H' is chicken burgers.

Step-by-step explanation:

The question involves setting up a system of equations to represent a real-world scenario involving the purchase of different types of burgers. In this scenario, 'P' represents the number of plain burgers, 'C' represents the number of cheeseburgers, and 'H' represents the number of chicken burgers. The total number of burgers ordered is 500, which gives us the first equation P + C + H = 500. The foundation ordered 100 fewer chicken burgers than plain burgers, so H = P - 100. The total cost for all the burgers is $1,172.50, which is represented by the second equation 1.75P + 2.50C + 3.20H = 1172.50.

The correct system of equations to represent this situation can be derived by combining these relationships. We can substitute H in the second equation with P - 100 to incorporate the relationship between the number of plain and chicken burgers. This will allow us to solve for P and C using the two equations provided. The correct option that represents this scenario is:

• P + C + H = 500
• 1.75P + 2.50C + 3.20H = 1172.50

This corresponds to Option A, as it correctly represents the total number of burgers and the total cost of the orders.