SOLUTION: (A linear system) Solve using matrix inverse method. (A^-1B=X) A-Bear's Catering service charges its customers according to the number of servings of each item that is supplied at

Question 108047: (A linear system) Solve using matrix inverse method. (A^-1B=X)
A-Bear's Catering service charges its customers according to the number of servings of each item that is supplied at the party. The table shows the number of servings of jambalaya, crawfish pie, file' gumbo, iced tea' and dessert for the last five customers along with the total cost of each party. What amount
does A-Bear's charge per serving of each item? Write all equations that would be used to solve this system.Be sure to define all variables.
Jambalaya Crawfish pie File' gumbo Iced tea Dessert cost
Boudreax 36 28 35 90 68 344.35
Thibodeaux 37 19 56 84 75 369.10
Fontenot 49 55 70 150 125 588.90
Arceneaux 58 34 52 122 132 529.50
Gautreaux 44 65 39 133 120 521.65
Write the matrix A=
write the matrix B=
write the matrix x=
This is a homework question that me and other classmates have been trying to figure out, but can't. We don't even know where to start.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Write all equations that would be used to solve this system.Be sure to define all variables.
........Jambalaya/ Crawfish pie/ File' gumbo/ Iced tea/ Dessert/ cost
Boudreax 36.......... 28........... 35.......... 90......68 .......344.35
Thibodeaux 37 19 56 84 75 369.10
Fontenot 49 55 70 150 125 588.90
Arceneaux 58 34 52 122 132 529.50
Gautreaux 44 65 39 133 120 521.65
Write the matrix A=
write the matrix B=
write the matrix x=
------------
Let unit price of Jambalaya be "a"; unit price of Crawfish pie be "b",
unit price of File gumbe be "c",......."d",......"e"
-------------------------
EQUATIONS:
36a +28b + 35c + 90d + 68e = 344.45
37a +19b + 56c + 84d + 75e = 369.90
etc.
Matrix A has all the coefficients:
36.......... 28...........35.........90......68
37...........19...........56.........84......75
etc.
--------------
Matrix B has all the cost numbers:
344.45
369.90
etc
-------------
Matrix "x" has all the answers:
a = 2.85
b = 1.85
c = 1.75
d = 0.75
e = 0.90
===========
Cheers,
Stan H.
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