Question

At a KFC outlet located in New Jersey, an order of 4 pieces of chicken, 2 servings of fries and 1 drink costs $24.00. A second order of 5 pieces of chicken, 3 servings of fries and 3 drinks costs $34.00. A third order of 9 pieces of chicken, 5 servings of fries and 2 drinks cost $55.00. Use Cramer's rule to calculate the cost of a piece of chicken, a serving of fries, and a drink: Define each variable.

Answer 1

The problem is a mathematical exercise in solving a system of linear equations with three variables representing the cost of chicken, fries, and a drink at a KFC outlet, using Cramer's rule.

Step-by-step explanation:

The student's question involves solving a system of linear equations using Cramer's rule to determine the price of individual items in a KFC order. Given the information, we can define three variables:

• c for the cost of a piece of chicken
• f for the cost of a serving of fries
• d for the cost of a drink

From the orders given, we set up the following system of linear equations:

1. 4c + 2f + d = 24
2. 5c + 3f + 3d = 34
3. 9c + 5f + 2d = 55

To use Cramer's rule, we first calculate the determinant (det) of the coefficient matrix, and then find the determinants of matrices where the respective column is replaced by the constants on the right side of each equation. This way, we obtain the individual prices when we divide each modified determinant by the original determinant.