Question

The Marks and Brog families are buying food for their neighbor's holiday party. The Marks family buys main course dishes for $5, and the Brog family is going to bring appetizers that cost $3. Together the families spend $64 on sixteen items of food. How many of each item are they bringing?

a) 8 main course dishes and 8 appetizers.
b) 10 main course dishes and 6 appetizers.
c) 6 main course dishes and 10 appetizers.
d) 16 main course dishes and 0 appetizers.

Answer 1

After setting up and solving simultaneous equations, it is found that the families are bringing 8 main course dishes and 8 appetizers to the holiday party.

Step-by-step explanation:

The question involves solving a simultaneous equations problem to figure out how many main course dishes and appetizers the Marks and Brog families are bringing to their neighbor's holiday party. Let's define main course dishes as 'm' that cost $5 each and appetizers as 'a' that cost $3 each. We have two equations based on the information provided:

1. 5m + 3a = $64 (total amount spent)
2. m + a = 16 (total items bought)

To solve these equations, we can multiply the second equation by 3 to line up the coefficients of 'a':

3m + 3a = 48

Now subtracting this from the first equation gives us:

5m + 3a - (3m + 3a) = 64 - 48

2m = 16

Dividing both sides by 2:

m = 8

Substituting m into the second equation:

8 + a = 16

a = 8

Therefore, they are bringing 8 main course dishes and 8 appetizers.