Question

Dwayne is throwing a summer kick-off party. He is making 25 bags of candy as party favors for his guests. Dwayne plans to put at most 10 taffies in each bag.
Let t represent the number of taffies that Dwayne might put in each bag. Which inequality models the story?
Graph the inequality that models the story.
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.

Answer 1

To model the situation with an inequality, we start by defining the variables. Let \( t \) represent the number of taffies in each bag. Dwayne plans to put at most 10 taffies in each bag, which can be expressed as:

\[
t \leq 10
\]

Now, this inequality indicates that the number of taffies \( t \) in each bag can be any value up to and including 10.

Next, let's graph the inequality \( t \leq 10 \):

1. **Draw the horizontal line** at \( t = 10 \).
2. **Since the inequality is less than or equal to (\( \leq \))**, we will use a **closed dot** on the line at \( t = 10 \) to indicate that 10 is included in the solution set.
3. **Since we are looking for the values of \( t \) that are less than or equal to 10**, we will shade the area **below the line**. This signifies all the values that are less than 10.

### Steps to Create the Graph:

- Draw a horizontal line parallel to the x-axis at \( t = 10 \).
- Place a closed dot (●) at \( t = 10 \).
- Shade the area below \( t = 10 \) indicating all values of \( t \) that are less than or equal to 10.

This graph visually represents the inequality \( t \leq 10 \), showing the maximum number of taffies Dwayne can put in each bag.

If you're using graphing software or tools, simply select the relevant features (like a line, dot, and shading) based on these instructions.