Question

The booster club is purchasing food for a banquet. They are expecting 180 guests, including adults and children. The cost of an adult meal is $5, and a children's meal is $3. The final bill is $740. How many adults and how many children are expected at the banquet?

Create a System of equations from the prompt ​

Answer 1

In order to find out how many adults and children are expected at the banquet, we establish a system of two equations based on the given costs and final bill. The first equation represents the total number of guests (A + C = 180) and the second represents the total cost of the meals (5A + 3C = 740). By solving the system, we can determine the numbers of adults and children attending.

Step-by-step explanation:

To solve the problem of how many adults and how many children are expected at the banquet based on the final bill and the cost of their meals, we need to create a system of equations. Let's denote the number of adults as A and the number of children as C.

The first equation represents the total number of guests:

A + C = 180

The second equation comes from the total cost of the meals:

5A + 3C = 740

System of equations:

• A + C = 180 (equation for total guests)
• 5A + 3C = 740 (equation for total cost)

To solve this system, you would typically use methods such as substitution or elimination to find the values of A and C.