Question
Polly is baking cookies for her friend's cookie swap. She wants to make a total of 50 cookies. Polly is short on raisins and can make no more than 20 raisin cookies; the rest will be chocolate chip.
Let r represent the number of raisin cookies that Polly might make. 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.
Let r represent the number of raisin cookies that Polly might make. 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.
Answers
GPT-4o mini
To model the situation described for Polly's cookie baking, let's define the variables and inequalities.
Let \( r \) represent the number of raisin cookies Polly makes. Since the total number of cookies she wants to make is 50, the number of chocolate chip cookies she will make can be expressed as \( 50 - r \).
According to the information provided:
1. She can make no more than 20 raisin cookies. This gives us the inequality:
\[
r \leq 20
\]
2. Additionally, since she can't make a negative number of cookies, we also have:
\[
r \geq 0
\]
Combining these inequalities, we have:
\[
0 \leq r \leq 20
\]
Now, to graph the inequality \( 0 \leq r \leq 20 \):
1. **Draw a number line**: This should include at least the range from 0 to 20.
2. **Mark the endpoints**:
- Since \( r \) can equal 0, you will put a closed dot or circle at 0.
- Since \( r \) can equal 20, you will also put a closed dot or circle at 20.
3. **Shade the region between the two points**: Shade along the line from 0 to 20 to indicate that \( r \) can take any value in this range.
Remember that since both endpoints are included, this is a closed interval. The final graph will show all possible values of `r` that Polly can use to make raisin cookies, ranging from 0 to 20.
> If you are doing this graphically on paper or a digital tool, you can choose the correct graphical representation and use the instructions for creating rays and endpoints as needed for your specific drawing tool.
Let \( r \) represent the number of raisin cookies Polly makes. Since the total number of cookies she wants to make is 50, the number of chocolate chip cookies she will make can be expressed as \( 50 - r \).
According to the information provided:
1. She can make no more than 20 raisin cookies. This gives us the inequality:
\[
r \leq 20
\]
2. Additionally, since she can't make a negative number of cookies, we also have:
\[
r \geq 0
\]
Combining these inequalities, we have:
\[
0 \leq r \leq 20
\]
Now, to graph the inequality \( 0 \leq r \leq 20 \):
1. **Draw a number line**: This should include at least the range from 0 to 20.
2. **Mark the endpoints**:
- Since \( r \) can equal 0, you will put a closed dot or circle at 0.
- Since \( r \) can equal 20, you will also put a closed dot or circle at 20.
3. **Shade the region between the two points**: Shade along the line from 0 to 20 to indicate that \( r \) can take any value in this range.
Remember that since both endpoints are included, this is a closed interval. The final graph will show all possible values of `r` that Polly can use to make raisin cookies, ranging from 0 to 20.
> If you are doing this graphically on paper or a digital tool, you can choose the correct graphical representation and use the instructions for creating rays and endpoints as needed for your specific drawing tool.