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 1196811: 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. Plan burgers each require 1 beef patty and 1 bun, double cheese burgers each require 2 beef patties, 1 bun, and 2 slices of cheese, while regular cheeseburgers each require 1 beef patty, 1 bun, and 1 slices of cheese. How many of each should be made?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52855) (Show Source): You can put this solution on YOUR website!
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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 cheese burgers each require 2 beef patties, 1 bun, and 2 slices of cheese, while regular cheeseburgers each require 1 beef patty, 1 bun, and 1 slices of cheese. How many of each should be made?
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Format the input information as I did it for easy reading. Then write a system of equations as you read the problem 1P + 2D + 1R = 15 (1) (counting beef patties) 1P + 1D + 1R = 12 (2) (counting buns) 0P + 2D + 1R = 11 (3) (counting slices of chees) Here P = # of Plain burgers, D = # of Double cheese burgers and R = # of Regular cheeseburgers. Next use your calculator, or free of charge online solvers, or your skills in solving matrix equations. I used an online solver at web-site www.reshish.com and got the answer X = 4, Y = 3, Z = 5. ANSWER. 4 Plain burgers, 3 Double cheese burgers and 5 regular cheeseburgers.

Solved, with explanations.

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The problem can be solved informally using logical reasoning, without algebra and without online calculators.

Each type of burger uses one bun, so the total number of burgers is 12.

All types of burger use at least one patty, and only the double cheeseburgers use two. Since there are 12 buns and 15 beef patties, the number of double cheeseburgers must be 15-12 = 3.

That means 12-3 = 9 of the burgers are either plain burgers or cheeseburgers. The three double cheeseburgers use 6 of the 11 slices of cheese, so there are 11-6 = 5 slices for the single cheeseburgers; that of course means there need to be 5 plain cheeseburgers.

3 double cheeseburgers and 5 plain cheeseburgers leaves 12-3-5 = 4 plain burgers.

ANSWERS: 3 double cheeseburgers, 4 plain burgers, and 5 regular cheeseburgers.

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