Question
Emily is making purple frosting to decorate cupcakes for her birthday party. She adds 8 drops of red food coloring to a bowl of white frosting. Emily wants the frosting to be a pinkish shade of purple, so she adds less blue food coloring than red food coloring.
Let b represent the number of drops of blue food coloring that Emily might add. Which inequality models the story?
Graph the inequality that models the story.
Let b represent the number of drops of blue food coloring that Emily might add. Which inequality models the story?
Graph the inequality that models the story.
Answers
GPT-4o mini
To model the relationship described in the story, we can denote the number of drops of blue food coloring Emily adds as \( b \). Since Emily wants the amount of blue food coloring to be less than the amount of red food coloring, and she adds 8 drops of red food coloring, we can express this with the inequality:
\[
b < 8
\]
This inequality indicates that the number of drops of blue food coloring \( b \) must be less than 8.
### Graphing the Inequality
To graph the inequality \( b < 8 \):
1. **Draw a number line**: Start by drawing a horizontal line with numbers marked on it. Make sure to include at least the number 8.
2. **Identify the boundary**: The boundary for our inequality is at \( b = 8 \).
3. **Use an open circle**: Since the inequality is strictly less than (<), we place an open circle at the point 8 on the number line to show that \( b = 8 \) is not included in the solution set.
4. **Shade the region**: Shade the line to the left of 8 to represent all values \( b \) that are less than 8.
The resulting graph will show an open circle at 8 and a shaded area extending to the left, representing all values \( b < 8 \).
\[
b < 8
\]
This inequality indicates that the number of drops of blue food coloring \( b \) must be less than 8.
### Graphing the Inequality
To graph the inequality \( b < 8 \):
1. **Draw a number line**: Start by drawing a horizontal line with numbers marked on it. Make sure to include at least the number 8.
2. **Identify the boundary**: The boundary for our inequality is at \( b = 8 \).
3. **Use an open circle**: Since the inequality is strictly less than (<), we place an open circle at the point 8 on the number line to show that \( b = 8 \) is not included in the solution set.
4. **Shade the region**: Shade the line to the left of 8 to represent all values \( b \) that are less than 8.
The resulting graph will show an open circle at 8 and a shaded area extending to the left, representing all values \( b < 8 \).