The Associated Students organization holds a Night at the Movies fundraiser. Students tickets are $1.00 each and nonstudent tickets are $4.00 each. The theater holds a maximum of 210 people. The club needs to collect at least $100 to make money. Let x represent students and y represent nonstudents. Shade the region in the first quadrant that contains all combinations of students and nonstudents that could attend the movie night so the club makes money.

Question

Quizplus · Accepted Answer

To make money, the club needs to collect at least $100. Let's set up an equation to represent this:

1x + 4y ≥ 100

We also know that the theater can hold a maximum of 210 people, so we have another equation:

x + y ≤ 210

To graph this, we can first graph the line x + y = 210, which represents the maximum number of people that can attend. This line goes through the points (0, 210) and (210, 0).

Next, we can graph the line 1x + 4y = 100 by finding the x and y intercepts:

x-intercept: 1x + 4(0) = 100 → x = 100

y-intercept: 1(0) + 4y = 100 → y = 25

So this line goes through the points (100, 0) and (0, 25).

Now we need to determine which region in the first quadrant (where x and y are positive) satisfies both equations. This region is shaded in choice D. Any point in this region represents a combination of students and nonstudents that could attend the movie night and allow the club to make money.

The Associated Students Organization Holds a Night at the Movies