# graphing, substitution, elimination, matrix

Part I (refer to the section on Systems of Linear Equations; Matrices in your text):

As a restaurant owner there are many decisions that you need to make on a daily basis, such as where to keep inventory levels. You wish to replenish your stock of dishes by purchasing 250 sets for your restaurant. You have two dish design from which to choose. One design costs $20 per set and the other $45 per set. If you only have $6,800 to spend, how many of each design should you order?

Hint:

Let x = the number of sets of $20 dishes and y = the number of sets of $45 dishes.

Solve the equations for the different dish designs to be ordered with the desired technique: graphing, substitution, elimination, matrix.

Explain how to check your solution for both equations.

https://brainmass.com/math/linear-algebra/graphing-substitution-elimination-matrix-354472

#### Solution Preview

Let x be the number of sets of $20 dishes and y be the number of sets of $45 dishes.

We need to buy 250 sets of dishes, so x+y=250. This is our first equation.

Now, for each set of $20-a-set dishes, we pay 20 dollars. And we buy x of these sets. So, for all sets of $20-a-set dishes we buy, we pay 20x dollars.

For each set of $45-a-set dishes, we pay $45 dollars. And we buy y of these sets. So, for all sets of $45-a-set dishes we buy, we pay 45y dollars.

In total we're prepared to pay 6,800 dollars, so the sums have to add up to ...

#### Solution Summary

Solve the equations for the different dish designs to be ordered with the desired technique: graphing, substitution, elimination, matrix. Explain how to check your solution for both equations.