SOLUTION: From the following augmented matrix, first write the system of equations that represents the augmented matrix and then create a real-world word problem that would represent these

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Question 106425: From the following augmented matrix, first write the system of equations that represents the augmented matrix and then create a real-world word problem that would represent these equations and their unknowns. Be creative. Do not use word problems that are in the assignments or course material. 
é1  1  1ùéxù    é100ù
ê5 -3  0úêyú = ê 10ú
ë0  3  4ûëzû    ë290û

Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
if we have this matrix:

[1,1,1][x]= [100]
[5,-3,0][y]= [10]
[0,3,4] [z]= [290]


the system of equations is:

x++%2B++y++%2B++z++=+100
5x++-+3y++++++++++=++10
+3y++%2B+4z+=+290

and a real-world word problem could be:

Three detectives named Mr. Clueless (let the number of cases the he has solved be x), Mr. Confused (let the number of cases the he has solved be y), and Mr. Smarty Pants (let the number of cases the he has solved be z) all together have solved 100 cold+cases.
Since Mr. Clueless is kind of "slow", his quintuple number of cases is 10 less then triple number of Mr. Confused cases. We also know that a sum+of triple number of Mr. Confused cases and quadruple number of Mr. Smarty Pants cases is 290.
What a number of cold+cases have each of them solved?


Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
From the following augmented matrix, first write the system of equations that represents the augmented matrix and then create a real-world word problem that would represent these equations and their unknowns. Be creative. Do not use word problems that are in the assignments or course material. 
é1  1  1ù éxù    é100ù
ê5 -3  0ú êyú = ê 10ú
ë0  3  4û ëzû    ë290û 

The system of equations is

1x + 1y + 1z = 100
5x - 3y + 0z =  10
0x + 3y + 4z = 290

or

 x +  y +  z = 100
5x - 3y      =  10
     3y + 4z = 290

John has three numbers written on a sheet of paper.  He observes
that their sum is 100. He then observes that the difference 
between five times the first number and three times the second 
number is 10. Finally he observes that three times the second 
number increased by four times the third number is 290.  What 
three numbers are written on John's piece of paper?

Answer: first number = 20, second number = 30, third number = 50.

Edwin