Question

Identify the graph that represents the amounts of fruit juice and ginger ale she can use, and identify a valid solution.

Answer 1

(24, 4)

Step-by-step explanation:

Let's call x the amount of fruit juice and y the amount of ginger ale.

Then, she plans to add at least 20 cups of fruit juice, which means that x is greater than or equal to 20, so

x ≥ 20

Additionally, the cup has a capacity of 32 cups, so the sum of the amounts x and y should be lower than or equal to 32, so

x + y ≤ 32

y ≤ 32 - x

Therefore, we need to graph the system of equations

x ≥ 20

y ≤ 32 - x

So the region will be on the right of the line x = 20 and below the line y = 32 - x as it is shown in the following graph

Finally, a valid solution is a point (x, y) = (24, 4) because it satisfies both equations

x ≥ 20

24 ≥ 20

y ≤ 32 - x

4 ≤ 32 - 24

4 ≤ 8