Vicki volunteers for 3-hour shifts at the library on the weekends. During the week, she volunteers for 2-hour shifts at a nursing home. She volunteers for more than 24 hours a week.

Question

Which of the following graphs represents this situation?

W.
X.

Y.
Z.
A.
X
B.
W
C.
Y
D.
Z

Answer 1

To analyze the problem, let's break down Vicki's volunteering schedule:

1. Vicki volunteers for 3-hour shifts at the library on weekends. Let \( x \) represent the number of shifts she works at the library on weekends. Therefore, her total hours from the library can be represented as \( 3x \).

2. Vicki also volunteers for 2-hour shifts at a nursing home during the week. Let \( y \) represent the number of shifts she works at the nursing home. Thus, her total hours from the nursing home can be represented as \( 2y \).

3. The total number of hours Vicki volunteers in a week is given by the equation: \[ 3x + 2y > 24 \]

Now, we need to determine which graph represents this inequality.

The graph representing \( 3x + 2y > 24 \) will have a boundary line of \( 3x + 2y = 24 \). The area above this line will represent the solutions where Vicki volunteers more than 24 hours a week.

Now, we need to identify the graphs W, X, Y, and Z based on how they represent this inequality. Without the visual details of the graphs provided, I can give you guidance on what to look for:

• Look for a line that intersects the axes in a way that supports the equation \( 3x + 2y = 24 \).
• The area above this line should be shaded, indicating that the total hours volunteered exceeds 24 hours.

If you have specific graph depictions for W, X, Y, and Z, please describe them, and I can assist you in identifying which one represents the inequality correctly.