5.2+Breaking+Even+0910

AP May 2, 2010  __Big Idea __: Negative numbers help us to model many real world situations.  __Essential Question __: How do I multiply and divide integers?   __Notes __: P= 60t – 800  P is Jean’s profit in dollars, and t is the number of tune-ups.  __<span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Journal Problem 5.2 __ <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> **<span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> # of tune-ups ** || **<span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Profit ** || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">0 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">-800 dollars || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">1 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">-740 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">2 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">-680 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">3 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">-620 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">4 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">-560 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">5 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">-500 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">6 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">-440 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">7 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">-380 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">8 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">-320 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">9 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">-260 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">10 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">-200 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">11 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">-140 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">12 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">-80 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">13 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">-20 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">14 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">40 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">15 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">100 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">16 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">160 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">17 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">220 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">18 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">280 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">19 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">340 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">20 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">400 || <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">
 * __<span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">5.2 __****<span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> – __Breaking Even__ **
 * <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">A) Make a table that shows the profit Jean will earn for 0 through 20 tune-ups. **
 * <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">B) Plot the (tune-ups, profit) data from your table on a coordinate grid. Be sure to label the axes. Explain how you chose the scale for each axis. **

<span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt; mso-no-proof: yes;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">I chose the scale for the x-axis - tune-ups by single units, because there are 20 tune-ups, and in my table, I did not skip any in between. For the y-axis – profit, I chose a scale of 60 because the profit increases by $60 each tune-up. <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> C) What will Jean’s profit be if she does only four tune-ups? How is this shown on the graph? ** <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">If Jean only does 4 tune-ups, her profit will be -560 dollars. On the graph, this is shown as a point on (4, -560), below the horizontal line. <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Jean will have to do 14 tune-ups before she breaks even. This is shown on the graph as a point on (14, 40), above the horizontal line. <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Jean’s profit increases by $60 with each tune-up she does. On the graph, this is shown as a points on the coordinate graph rising in a linear pattern. <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> __<span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Journal Problem 5.2 Follow Up __ <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">The break-even point for this profit equation is 11 tune-ups. <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">The break-even point for this profit equation is 21 tune-ups. <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">
 * <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">
 * <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">D) How many tune-ups will Jean have to do before she breaks even? How is this shown on the graph? **
 * <span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">E) How does Jean’s profit change with each tune-up she does? How is this shown on the graph? **
 * 1. ****<span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">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 profit equation? **
 * 2. ****<span style="font-family: "Times New Roman"; font-size: 14.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">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 profit equation? **