Question

He profit on the sale of a small bag of popcorn is $1, while the profit on the sale of a medium bag of popcorn is $2. The Glee Club expects to sell fewer than 100 total bags of popcorn, but they hope to make more than $100 in profit. The system that represents this is s+m<100 and s+2m>100. The graph of the boundary lines is shown below. Which regions should be shaded (to form the solution)?
HELP ME PLEASE

Select one:
a. 1 and 2
b. 1 only
c. 2 only
d. 3 only

Answer 1

The first inequality is represented by the line with the y intercept of 100 (the "top" line). We need to pick a region that satisfies the inequality. Let's try the point (0, 0). If we sub in 0 for x and 0 for y, the inequality would look like this: 0 + 0 < 100. Is 0 less than 100? Yes of course it is. So the regoins that satisfy that inequality are regions 1 and 2. Now for the second inequality. Obviously, it is the other line, the "bottom" line with the y intercept of 50. If we sub in the same point of (0, 0), subbing in looks like this: 0 + 2(0) > 100. Is 0 greater than 100? Of course it's not. So the regions that satisfy this inequality are regions 2 and 3. The solution to an inequality is where the shading overlaps. For us that is in region 2 only. Your choice for the answer is c