Tess is buying beverages for her annual end-of-summer party. Cases of water cost $3.75, and cases of soda cost $5. Tess wants to spend less than $30 on beverages.

Question

This graph shows how many cases of water, x, and cases of soda, y, Tess can buy for her party.

Answer 1

We can create two inequalities to represent the situation:

3.75x + 5y < 30 (Total cost of beverages must be less than $30)
x, y ≥ 0 (Cannot buy negative cases)

We then need to graph these inequalities on a coordinate plane. Since this is a linear inequality, we can solve for y in terms of x to graph it easily.

For 3.75x + 5y < 30:
5y < 30 - 3.75x
y < 6 - 0.75x

First, graph the line y = 6 - 0.75x (dashed line, since it doesn't include the points on the line) and then shade in the area below it. This will give the feasible region where Tess can spend less than $30 on beverages.