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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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      Log On


   

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) About Me  (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:
p= number of plain burgers,
c= number of cheeseburgers,
d= number of double cheeseburgers.
(Some people like to use x , y, and z
but I like variable names that remind of their meaning).

All the burgers require 1 bun per burger,
so p%2Bc%2Bd buns are needed,
and 14%2A8 buns are available(14 packs of 8 buns per pack).
That gives us the equation
p%2Bc%2Bd=14%2A8 , or p%2Bc%2Bd=112 .

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
p%2Bc%2B2d ,
and 12%2A12 patties area available (12 packs, with 12 frozen hamburger patties per pack).
That gives us the equation
p%2Bc%2B2d=12%2A12 , or p%2Bc%2B2d=144 .

A plain hamburger requires no cheese,
while a cheeseburger requires one slice of cheese,
and a double cheeseburger required 2 slices,
so c%2B2d slices of cheese will be needed.
There area 3%2A24 slices of cheese available (3 packs, with 24 slices per pack),
and that gives us the equation
c%2B2d=3%2A24 or c%2B2d=72 .

The three equation form the easy system of linear equations
system%28p%2Bc%2Bd=112%2Cp%2Bc%2B2d=144%2Cc%2B2d=72%29 .
Subtracting the first equation from the second, we get
highlight%28d=32%29 .
Substituting that value in the third equation we get
c%2B2%2A32=72 --> c%2B64=72 --> c=72-64 --> highlight%28c=8%29 .
Substituting the values found for c and d into the first equation we get
p%2B8%2B32=112 --> p%2B40=112 --> p=112-40 --> highlight%28p=72%29 .

plain hamburgers 72
cheeseburgers 8
double cheeseburgers 32.