SOLUTION: A plain hamburger requires one ground beef patty and a bun. A cheeseburger requires one ground beef patty, one slice of cheese, and a bun. A double cheeseburger requires two ground

Question 1029850: A plain hamburger requires one ground beef patty and a bun. A cheeseburger requires one ground beef patty, one slice of cheese, and a bun. A double cheeseburger requires two ground beef patties, two slices of cheese, and a bun.
Frozen hamburger patties are typically sold in packs of 12; hamburger buns, in packs of 8; and cheese slices, in packs of 24.
A family is in charge of providing burgers for a neighborhood block party. They have purchased 14 packs of buns, 12 packs of hamburger patties, and 3 packs of cheese slices. How many of each type of sandwich should they make if they want to use up all of the buns, patties, and cheese slices?
plain hamburgers _____
cheeseburgers ______
double cheeseburgers ______

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
We start by giving variable names that will work as placeholders for the values we need to find:
= number of plain burgers,
= number of cheeseburgers,
= number of double cheeseburgers.
(Some people like to use , , and
but I like variable names that remind of their meaning).

All the burgers require bun per burger,
so buns are needed,
and buns are available(14 packs of 8 buns per pack).
That gives us the equation
, or .

The plain burgers, and the cheeseburgers require one patty each,
but each double cheeseburger required 2 patties,
so the number of frozen hamburger patties required is
,
and patties area available (12 packs, with 12 frozen hamburger patties per pack).
That gives us the equation
, or .

A plain hamburger requires no cheese,
while a cheeseburger requires one slice of cheese,
and a double cheeseburger required 2 slices,
so slices of cheese will be needed.
There area slices of cheese available (3 packs, with 24 slices per pack),
and that gives us the equation
or .

The three equation form the easy system of linear equations
.
Subtracting the first equation from the second, we get
.
Substituting that value in the third equation we get
--> --> --> .
Substituting the values found for and into the first equation we get
--> --> --> .

plain hamburgers 72
cheeseburgers 8
double cheeseburgers 32.
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