5.2+Breaking+Even+0910+0910

Tune-ups || Profit || 0 ||   -800  ||  1  ||   -740  ||  2  ||   -680  ||  3  ||   -620  ||  4  ||   -560  ||  5  ||   -500  ||  6  ||   -440  ||  7  ||   -380  ||  8  ||   -320  ||  9  ||   -260  ||  10  ||   -200  ||  11  ||   -140  ||  12  ||   -80  ||  13  ||   -20  ||  14  ||   40  ||  15  ||   100  ||  16  ||   160  ||  17  ||   220  ||  18  ||   280  ||  19  ||   340  ||  20  ||   400  ||
 * SC **
 * May 15, 2010 **
 * Math 7B **
 * Big Idea: Negative Numbers help us to model many real world situations. **
 * Essential Question: How do I multiply and divide integers? **
 * Problem 5.2: Breaking Even **
 * A.  ****  Make a table that shows the profit Jean will earn for 0-20 tune-ups.  **

I chose this scale because it fit all the numbers into one graph and followed the pattern of the tune-ups (going up by 60 each time). After 4 tune-ups Jean’s profit is $-560. On the graph you can go over 4, and see that under that the amount of money is $-560. It is $-560 because at first she had $-800 but then she did 4 tune-ups and earned $260, so $-800+$260=$-560. Jean will have to do 14 tune-ups before she breaks even. This is shown on the graph because this is the point where the line passes through to the first quadrant, where you now start to have positive numbers. Jean charges $60 for each tune-up, so each time her profit changes by $60. On the graph you can see that with each tune-up she does her profit is increasing. You can see her profit is increasing because the line on the graph moves onto the positive quadrant and then keeps on moving diagonally. The break-even point is 10, because, P=60x10-600=0. After 10 tune-ups Jean will have reached $0 and then finally start making profit. The break-even point for this equation would just be double because you are just doubling the costs. So, the break-even point would be 20, P=60x20-1200=0.
 * B.  ****  Plot the (tune-ups, profit) data from your table on a coordinate graph. Be sure to label the axis. Explain how you chose the scale for each axis.[[image:Capture.JPG]]  **
 * C. **** What will Jean’s profit be if she only does 4 tune-ups? How is this shown on the graph? **
 * D. **** How many tune-ups will Jean have to do before she breaks even? How is this shown on the graph?  **
 * E. **** How does Jean’s profit change with each tune-up she does? How is this shown on the graph? **
 * Follow Up **
 * 1. **** Jean figures out that she could decrease her start up cost to $600 by buying used tools. She writes a new equation, P=60t-600, to determine her profit. What is the break-even point for this equation?  **
 * 2. ** **Jean’s friend Chuck, thinks Jean should advertise her business in the local paper. This would increase her costs, giving her the profit equation P=60t-1200. What is the break-even point** **for this equation?**