Final answer:
To find the cost of each item, assign variables to the cost of a cheeseburger and a package of fries. Then set up a system of equations and represent them using matrices. Use matrix operations to solve for the variables and find the cost of each item. Therefore, the cost of each cheeseburger is $11.7 and the cost of each package of fries is $14.85.
Step-by-step explanation:
To solve this problem using matrices, let's assign variables to the cost of each item. Let 'x' represent the cost of a cheeseburger and 'y' represent the cost of a package of fries. We can then set up a system of equations using the given information:
Equation 1: 3x + 2y = 10.95
Equation 2: 6x + 5y = 23.85
To solve this system of equations, we can represent it using matrices:
[3 2][x] [10.95]
[6 5][y] = [23.85]
Using matrix operations, we can calculate the values of 'x' and 'y' by multiplying the inverse of the coefficient matrix by the constant matrix. The inverse of the coefficient matrix is:
[3 2]^-1 = [5 -2]
[6 5] [-3 3]
Multiplying the inverse by the constant matrix:
[5 -2][10.95] [5(10.95) + (-2)(23.85)] [11.7]
[-3 3] [23.85] = [-3(10.95) + 3(23.85)] [14.85]
Therefore, the cost of each cheeseburger is $11.7 and the cost of each package of fries is $14.85.