# How would I represent this problem as three linear equations

• ambitionz
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] ambitionz said: ## 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.

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?