Question

Your family goes to a southern style restaurant for dinner. There are 6 people in your family. Some order the chicken dinner $14 and some order the steak dinner for $17. if the total bill was $99 how many people order each dinner?

Answer 1

Let's define two variables:

- Let \( c \) be the number of chicken dinners ordered.
- Let \( s \) be the number of steak dinners ordered.

We know the following:

1. The total number of dinners ordered is equal to the number of people in the family:
\[
c + s = 6
\]

2. The total cost of the dinners is $99, so:
\[
14c + 17s = 99
\]

Now we have a system of two equations:

1. \( c + s = 6 \)
2. \( 14c + 17s = 99 \)

We can solve this system using substitution or elimination. Let's use substitution.

From the first equation, we can solve for \( s \):
\[
s = 6 - c
\]

Now, substitute \( s \) into the second equation:
\[
14c + 17(6 - c) = 99
\]

Distributing the 17 gives:
\[
14c + 102 - 17c = 99
\]

Now, combine like terms:
\[
-3c + 102 = 99
\]

Subtract 102 from both sides:
\[
-3c = 99 - 102
\]
\[
-3c = -3
\]

Now, divide by -3:
\[
c = 1
\]

Now that we have \( c \), we can find \( s \) using the first equation:
\[
s = 6 - c = 6 - 1 = 5
\]

Thus, the solution is:
- **1 person ordered the chicken dinner.**
- **5 people ordered the steak dinner.**

To verify:
The total cost for 1 chicken dinner is \( 1 \times 14 = 14 \).
The total cost for 5 steak dinners is \( 5 \times 17 = 85 \).
Adding these gives \( 14 + 85 = 99 \), which matches the total bill.

So the answer is correct:
- \( c = 1 \) and \( s = 5 \).