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.

Question

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.