# How would I represent this problem as three linear equations

1. Feb 6, 2015

### ambitionz

1. The problem statement, all variables and given/known data

"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 . "

2. Relevant equations

How would I represent this problem as three linear equations

3. 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?

2. Feb 6, 2015

### Dick

Yes, that looks perfectly fine. If you are able to solve it algebraically for the correct answer, why would you doubt it?