How would I represent this problem as three linear equations

In summary: The only thing you might want to add is a statement of the problem itself as the first equation, just to make it clear what you are solving for: x + y + z = total number of machines2000x+500y+5000z = $280,000y = 5xx = 2z
  • #1
ambitionz
7
0

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]
 
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  • #2
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.

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?
 

Related to How would I represent this problem as three linear equations

1. How do I determine which variables to use in my linear equations?

To determine which variables to use, you must first identify the key components of the problem. These components can be represented as variables in your equations. For example, if the problem involves finding the total cost of buying a certain number of items, you may use variables such as "total cost" and "number of items" in your equations.

2. What is the process for writing three linear equations for a problem?

The process for writing three linear equations involves identifying the key components of the problem and representing them as variables. Next, you must determine the relationship between these variables, such as if they are directly proportional or inversely proportional. Finally, you can use the general form of a linear equation, y = mx + b, to write three equations by substituting the values of the variables.

3. Can I use more or less than three linear equations to represent a problem?

Yes, depending on the complexity of the problem, you may need to use more or less than three linear equations. In some cases, a single linear equation may be sufficient to represent the problem. However, if the problem involves multiple variables and relationships between them, it may require more than three equations to accurately represent it.

4. How do I know if my three linear equations are correct?

You can check the accuracy of your equations by solving them simultaneously. This means finding the values of the variables that satisfy all three equations. You can also plot the equations on a graph and see if they intersect at a common point, which would indicate that they are correct.

5. Are there any tips for making the process of writing three linear equations easier?

One tip is to clearly label and define your variables before writing the equations. This will help you keep track of which variables represent which components of the problem. Additionally, it can be helpful to use a system of equations, where one equation builds on the previous one, to ensure that all three equations are related and accurately represent the problem.

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