Your familygoes to a southern system restaurant for dinner there are 6 people in your family.

Question

Some order the chicken dinner for $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 denote the number of people who ordered chicken as \( x \) and the number of people who ordered steak as \( y \). We know the following:

1. The total number of people: \[ x + y = 6 \]

2. The total cost of the dinners: \[ 14x + 17y = 99 \]

Now, we can solve these equations step by step.

First, from the first equation, we can express \( y \) in terms of \( x \): \[ y = 6 - x \]

Next, we substitute \( y \) into the second equation: \[ 14x + 17(6 - x) = 99 \]

Expanding the equation: \[ 14x + 102 - 17x = 99 \]

Combine like terms: \[ -3x + 102 = 99 \]

Now, isolate \( x \): \[ -3x = 99 - 102 \] \[ -3x = -3 \] \[ x = 1 \]

Now that we have \( x \), we can find \( y \): \[ y = 6 - x = 6 - 1 = 5 \]

Thus, the solution is:

• Number of people who ordered chicken: \( 1 \)
• Number of people who ordered steak: \( 5 \)

To verify:

Total cost: \[ 14(1) + 17(5) = 14 + 85 = 99 \]

This confirms that the calculations are correct. Therefore, the final answer is:

• 1 person ordered chicken and 5 people ordered steak.