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 \( s = 5 \).