For the Spring Festival, the Math Club is selling rulers for $\$1$ and compasses for $\$2.50$.  

1. While the club would like to sell as many items as they can to raise funds, they need to make at least $\$15.00$ to break even. Write an inequality to represent this situation. Let $r=$ the number of rulers sold and $c=$ the number of compasses sold.

   Answer (a):

   $r+\$2.50c\ge\$15.00$

2. School rules state that the club can sell a maximum of $25$ items for the festival. Write an inequality for this constraint (limitation).

   Answer (b):

   $r+c\le25$

3. Graph the inequalities from parts (a) and (b) on the same set of axes so that compasses are represented on the $x$-axis and rulers are represented on the $y$-axis. Find the region of points that are solutions to each of them. Can this region fall below the $x$-axis or to the left of the $y$-axis? Why or why not?

   Hint (c):

   Test a point on one side of each line in order to find out what side must be shaded.

4. What do the points in the solution region represent?

   Hint (d):

   The shaded region represents all of the points that satisfy both inequalities.

   Use the blank expression lines in box 8 and 9 in the eTool below to graph the inequalities.
   Click on the link at right for the full eTool version: 9-110 HW eTool