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Question 1196188: I am not sure on what my teacher meant by wanting us to do this type problem with matrix which Iam confused about but here is the problem
Write and solve the system of linear equations.
Jason is helping raise money for a dog rescue foundation by selling baskets of dog treats.
•Basket A contains 4 peanut butter treats,3 bacon treats,and 2 cheese treats and sells for $12.31.
•Basket B contains 3 peanut butter treats,4 bacon treats,and 3 cheese treats and sells for $11.91.
•Basket C contains 6 peanut butter treats,5 bacon treats,and 4cheese treats and sells for $20.25
What is the cost for one of each kind of treat?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Write and solve the system of linear equations.
Jason is helping raise money for a dog rescue foundation by selling baskets of dog treats.
•Basket A contains 4 peanut butter treats,3 bacon treats,and 2 cheese treats and sells for $12.31.
•Basket B contains 3 peanut butter treats,4 bacon treats,and 3 cheese treats and sells for $11.91.
•Basket C contains 6 peanut butter treats,5 bacon treats,and 4cheese treats and sells for $20.25
What is the cost for one of each
================================================
4B + 3T + 2C = 1231 - Eqn 1
3B + 4T + 3C = 1191 - Eqn 2
6B + 5T + 4C = 2025 - Eqn 3
------------------
Solve for B, T & C
There's no mystery.
========================================
Using Elimination:
8B + 6T + 4C = 2462 - Eqn1 times 2
6B + 5T + 4C = 2025 - Eqn 3
-------------------------------------- Subtract
2B + T = 437 ----- C is eliminated --> Eqn A
=================
12B + 9T + 6C = 3693 - Eqn 1 times 3
6B + 8T + 6C = 2382 - Eqn 2 times 2
-------------------------------------- Subtract
6B + T = 1311 Eqn B
2B + T = 437 Eqn A
---------------------- Subtract
4B = 874
B = 218.5
---------
Sub for B in Eqn A
2B + T = 437 Eqn A
T = 0
-------
Sub for B and T in any equation:
4B + 3T + 2C = 1231 - Eqn 1
874 + 0 + 2C = 1231
2C = 357
C = 178.5
====================
Seems odd that B and C give 1/2 cent result, and that T's are free.
Answer by ikleyn(52788)  (Show Source):
You can put this solution on YOUR website! .
I am not sure on what my teacher meant by wanting us to do this type problem with matrix
which Iam confused about but here is the problem
Write and solve the system of linear equations.
Jason is helping raise money for a dog rescue foundation by selling baskets of dog treats.
•Basket A contains 4 peanut butter treats,3 bacon treats,and 2 cheese treats and sells for $12.31.
•Basket B contains 3 peanut butter treats,4 bacon treats,and 3 cheese treats and sells for $11.91.
•Basket C contains 6 peanut butter treats,5 bacon treats,and 4cheese treats and sells for $20.25
What is the cost for one of each kind of treat?
~~~~~~~~~~~~~~~~~
The major purpose of this problem (as I see it) is to teach you to write the corresponding matrix equation.
Let x be the price for one peanut butter treat,
y be the price for one bacon treat,
and z be the price for one cheese treat.
Then you write the system of equations for each basket separately, as you read the problem
4x + 3y + 2z = 12.31, (1)
3x + 4y + 3z = 11.91, (2)
6x + 5y + 4z = 20.25. (3)
If you do understand how this system of equations is build,
then more than half of the problem is just completed, absorbed and mastered.
I do not know what your teacher wants further from you.
May be, he (or she) wants you use your calculator to input the numbers and get the solution.
As for me, I will use one of numerous online solvers in the Internet from web-site
www.reshish.com
I input the matrix there and quickly get the answer x = 2.185, y = 0 and z = 1.785.
I don't know how to interpret these numbers with 3 decimal digits after the decimal point
(where, according to common sense, should be only two digits) in the context of the given problem.
From my side, I checked the answer using Excel spreadsheet, and found it absolutely and precisely correct.
I don't know how to interpret it in cents . . .
It is all that I think and all that I can say about this problem.
My warmest greetings to your teacher ( ! )
If you did learn nothing useful from my post,
it means that I spent my time for nothing.
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