SOLUTION: You own a hamburger franchise and are planning to shut down operations for the day, but you are left with 12 buns, 15 defrosted beef patties, and 11 opened cheese slices. Rather th

Question 1116909: You own a hamburger franchise and are planning to shut down operations for the day, but you are left with 12 buns, 15 defrosted beef patties, and 11 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?
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

let x = number of regular burgers
let y = number of double cheeseburgers
let z = number of regular cheeseburgers

Then

(1) x+y+z = 12 (the bun equation)
(2) x+2y+z = 15 (the patty equation)
(3) 2y+z = 11 (the cheese equation)

There are many ways of solving systems of 3 equations; but for this one the equations are so similar that solving the system is simple.

Comparing (1) and (2), we can see that y=3
Comparing (2) and (3), we can see that x=4
Then with x=4 and y=3, (1) tells us that z=5

Answer: 4 regular; 3 double cheese; 5 regular cheese
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