Question

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? •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.

Answer 1

1) 20x + 45y = 6800
2) 20(250 - y) + 45y = 6800 {multiply 20 through the parentheses}
3) 5000 - 20y + 45y = 6800 {combine the y terms 45y - 20y = 25y}
4) 5000 + 25y = 6800 {subtract 5000 from both sides}
5) 25y = 1800 {divide 25 from both sides}
6) y = 72

Now put y back into equation 1) x + y = 250

1) x + 72 = 250
2) x = 250 - 72
3) x = 178

Answer 2

To check, put both values back into the second equation.

20(178) + 45(72) = 6800

3560 + 3240 = 6800