You own a hamburger franchise and are planning to shut down

You own a hamburger franchise and are planning to shut down operations for the day, but you are left with 11 bread rolls, 13 defrosted beef patties, and 8 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.]

Solution

let plane burger = x

double cheeseburger = y

regualr cheeseburger = z

then

x + 2y + z = 13

x + y + z = 11

2y + z = 8

using equation 2) in 1)

y + 11 = 13 => y = 2

z = 8 - 2y = 4

x = 11 - y - z = 5

So

plane burger = 5

double cheeseburger = 2

regualr cheeseburger = 4