You own a hamburger franchise and are planning to shut down operations for the d

Question

You own a hamburger franchise and are planning to shut down operations for the day, but you are left with 9 buns, 13 defrosted beef patties, and 10 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 bun, double cheeseburgers each require 2 beef patties, 1 bun, and 2 slices of cheese, while regular cheeseburgers each require 1 beef patty, 1 bun, and 1 slice of cheese. How many of each should you make? HINT [See Example 1. plain burgers double cheeseburgers regular cheeseburgers

Explanation / Answer

Answer:

Let (a,b,c), where a,b,c are the numbers of beef patty, bun and slice of cheese required for each type of burger.

For plain burger it is (1,1,0), for double cheese burger it is (2,1,2) and for regular cheese burger it is(1,1,1).

Let x, y, z be the required nos. of plain burger,double cheese burger and regular cheese burger .Then,

x(1,1,0)+y(2,1,2)+z(1,1,1)=(13,9,10)

solving the above equation we get x=3,y=4 and z=2.

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