Question

You own a hamburger franchise and are planning to shut down operations for the day, but you are left with 13 bread rolls, 18 defrosted beef patties, and 12 opened cheese slices. Rather than throw them out, you decide to use them to make burgers that you will sell at a discount. Plain burgers each require 1 beef patty and 1 bread roll, double cheeseburgers each require 2 beef patties, 1 bread roll, and 2 slices of cheese, while regular cheeseburgers each require 1 beef patty, 1 bread roll, and 1 slice of cheese. How many of each should you make? HINT [See Example 1.]

plain burgers
double cheeseburgers
regular cheeseburgers

Answer 1

Let x be the no. of plain burger
Let y be the no. of double cheese burger
Let z be the no. of regular cheese burger

From the information provided we have the following equation.

beef patties : x+2y+z = 18
bread rolls : x + y +z = 13
cheese rolls : 2y+z = 12

We use Cramer's rule to solve these matrics.

We put the equation in a matrix as shown below.

1. We find the determinant of the coefficient matrix

2. We replace x column with answer column and then find the determinant (Dx)

3. We replace y column with answer column and then find the determinant (Dy)

4. We replace z column with answer column and then find the determinant (Dz)

We know that the Cramer rule says the following

Hence we have