How would I represent this problem as three linear equations

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Homework Statement



"A company has a budget of $280,000 for computing equipment. Three
types of equipment are available: microcomputers at $2000 a piece,
terminals at $500 a piece, and word processors at $5000 a piece. There
should be five times as many terminals as microcomputers and two
times as many microcomputers as word processors. Set this problem up
as a system of three linear equations. Determine approximately how
many machines of each type there should be by solving by trial-and-error.

Note: Check your answer by expressing the numbers of terminals and
microcomputers in terms of the number of word processors and solving
the remaining single equation in one unknown . "
[/B]


Homework Equations



How would I represent this problem as three linear equations[/B]

The Attempt at a Solution



I believe that I was able to solve the problem algebraically : number of microcomputers 40, number of word processors is 20, and the number of terminals is 200 but I'm not sure about how to express it as a series of three linear equations.

So far this is what I have :
Let x be the number of microcomputers
Let y be the number of terminals
Let z be the number of word processors

2000x+500y+5000z = 280,000
y = 5x
x = 2z

Should the previous three lines suffice?[/B]
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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Homework Statement



"A company has a budget of $280,000 for computing equipment. Three
types of equipment are available: microcomputers at $2000 a piece,
terminals at $500 a piece, and word processors at $5000 a piece. There
should be five times as many terminals as microcomputers and two
times as many microcomputers as word processors. Set this problem up
as a system of three linear equations. Determine approximately how
many machines of each type there should be by solving by trial-and-error.

Note: Check your answer by expressing the numbers of terminals and
microcomputers in terms of the number of word processors and solving
the remaining single equation in one unknown . "
[/B]


Homework Equations



How would I represent this problem as three linear equations[/B]

The Attempt at a Solution



I believe that I was able to solve the problem algebraically : number of microcomputers 40, number of word processors is 20, and the number of terminals is 200 but I'm not sure about how to express it as a series of three linear equations.

So far this is what I have :
Let x be the number of microcomputers
Let y be the number of terminals
Let z be the number of word processors

2000x+500y+5000z = 280,000
y = 5x
x = 2z

Should the previous three lines suffice?[/B]
Yes, that looks perfectly fine. If you are able to solve it algebraically for the correct answer, why would you doubt it?
 

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