Final answer:
To solve this problem, assign variables to represent the number of people who ordered chicken and steak. Set up a system of equations using the given information and solve for the variables. The correct answer is 3 people ordered chicken and 3 people ordered steak.
Step-by-step explanation:
To solve this problem, let's assign variables to represent the number of people who ordered chicken and steak. Let's call the number of people who ordered chicken 'x' and the number of people who ordered steak 'y'.
We know that there are 6 total people in the family, so x + y = 6.
We also know that the cost of the chicken meals is $16 and the cost of the steak meals is $17.50. The total bill is $84.50, so 16x + 17.50y = 84.50.
Now we can solve this system of equations to find the values of x and y. From the first equation, we can rearrange it to y = 6 - x. Substituting this into the second equation, we have 16x + 17.50(6 - x) = 84.50.
Solving this equation gives us x = 3 and y = 6 - 3 = 3.
Therefore, 3 people ordered chicken and 3 people ordered steak. So the correct answer is option c) 3 people ordered chicken, and 3 people ordered steak.