Chapter 5 Cooperative Learning

In this chapter, you learned how to graph relations and determine whether the relation is a linear equation. Once a relation has been graphed, the process of analyzing it to determine more applicable information is necessary in order to completely understand the problem or situation.

In this project, imagine that your family owns a catering business and you want to look at the amount that you charge for banquets. You have been asked to present your findings to the other members of your family that shows recommended charges and how they will affect your profit. After some research, you find that the initial basic charge for a banquet should be $250 plus $4 per person. Your food costs per person are $2.50, and your other costs such as labor, time, etc. total $1.00 per person.

Follow these steps to organize your results.

1. Determine the charges for various banquet sizes by creating a table using increments of 25 people.

Write one algebraic equation of the charges, y, for a banquet of x number of people.

2. Determine the costs for various banquet sizes again by creating a similar table.

Write one algebraic equation of the costs, y, for a banquet of x number of people.

3. Display your results on one graph. (Be sure to label each line and the axes.)

4. Write a paragraph of your mathematical interpretation of the graph. Be sure to discuss things like:

· Will the lines ever intersect? What does this mean for the company? Or for the average person?

· How do the first points you plotted for each line differ? Explain.

· Would it make sense to extend the graph into the other quadrants? Explain.

· Which of the three methods (table, equation, graph) is the most useful to the average person? Or to the company? Explain.