Question
Mona is having a bake sale this weekend and will make a total of 24 cupcakes to sell. She plans to make at most 12 vanilla cupcakes, and the rest will be chocolate cupcakes.
Let v represent the number of vanilla cupcakes Mona 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 v represent the number of vanilla cupcakes Mona 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
Answered by
GPT-4o mini
To model the situation described, we can set up the following inequality. Since Mona plans to make a total of 24 cupcakes and will make at most 12 vanilla cupcakes, we can express this with the following inequality:
\[ v \leq 12 \]
Where:
- \( v \) represents the number of vanilla cupcakes.
Additionally, since she will make a total of 24 cupcakes, the number of chocolate cupcakes would be \( 24 - v \). We also know that \( v \) must be at least 0 because she can't make a negative number of cupcakes. Therefore, we can state:
\[ 0 \leq v \leq 12 \]
So, the primary inequality modeling the number of vanilla cupcakes is:
\[ v \leq 12 \]
where \( v \) must also be greater than or equal to 0.
To graph this inequality:
1. Draw a number line.
2. Place a point at \( v = 12 \). Because the inequality uses \( \leq \), this point will be solid (indicating that 12 is included).
3. Shade the region to the left of 12 (down to 0) to represent all values of \( v \) that are less than or equal to 12.
4. Place a point at \( v = 0 \). This point is also solid since \( v \) must be greater than or equal to 0.
Final representation on the number line would show:
- A closed circle on \( v = 12 \) and \( v = 0 \)
- A shaded region from \( v = 0 \) to \( v = 12 \).
If you were to visualize this, you would see a horizontal line starting from \( v = 0 \) up to \( v = 12 \), including both endpoints.
\[ v \leq 12 \]
Where:
- \( v \) represents the number of vanilla cupcakes.
Additionally, since she will make a total of 24 cupcakes, the number of chocolate cupcakes would be \( 24 - v \). We also know that \( v \) must be at least 0 because she can't make a negative number of cupcakes. Therefore, we can state:
\[ 0 \leq v \leq 12 \]
So, the primary inequality modeling the number of vanilla cupcakes is:
\[ v \leq 12 \]
where \( v \) must also be greater than or equal to 0.
To graph this inequality:
1. Draw a number line.
2. Place a point at \( v = 12 \). Because the inequality uses \( \leq \), this point will be solid (indicating that 12 is included).
3. Shade the region to the left of 12 (down to 0) to represent all values of \( v \) that are less than or equal to 12.
4. Place a point at \( v = 0 \). This point is also solid since \( v \) must be greater than or equal to 0.
Final representation on the number line would show:
- A closed circle on \( v = 12 \) and \( v = 0 \)
- A shaded region from \( v = 0 \) to \( v = 12 \).
If you were to visualize this, you would see a horizontal line starting from \( v = 0 \) up to \( v = 12 \), including both endpoints.