Question
The sixth-grade classes at Sherwood Middle School raised money to donate to their local community center. Ms. Chen's class raised $146 with their car wash fundraiser. Mr. Vance's class had a bake sale and raised more money than Ms. Chen's class.
Let v represent the amount of money, in dollars, that Mr. Vance's class might have raised. Which inequality models the story?
Graph the inequality that models the story.
Let v represent the amount of money, in dollars, that Mr. Vance's class might have raised. Which inequality models the story?
Graph the inequality that models the story.
Answers
GPT-4o mini
To model the scenario described, we need to represent Mr. Vance's class's fundraising amount, \( v \), in relation to the amount raised by Ms. Chen's class, which is $146.
The statement mentions that Mr. Vance's class raised more money than Ms. Chen's class. This can be represented mathematically as:
\[
v > 146
\]
This inequality shows that the amount \( v \) must be greater than 146.
### Graphing the Inequality
To graph the inequality \( v > 146 \):
1. **Draw a number line**: Label it with values that include at least 140 to 160 for reference.
2. **Identify the boundary point**: At \( v = 146 \), make a hollow (open) circle, indicating that 146 is not included in the solution.
3. **Shade the appropriate region**: Since \( v \) is greater than 146, you would shade to the right of the open circle to indicate all the values that are greater than 146.
Here is a visual representation:
```
<---|---|----|----|----|----|----|----|----|----|----|---->
140 141 142 143 144 145 (146) 147 148 149 150 151 152 153 154 155 156
- - - - - - - O - - - - - - - - - - (shaded to the right)
```
The shaded area indicates all the values greater than 146, thus representing the amount of money raised by Mr. Vance's class.
The statement mentions that Mr. Vance's class raised more money than Ms. Chen's class. This can be represented mathematically as:
\[
v > 146
\]
This inequality shows that the amount \( v \) must be greater than 146.
### Graphing the Inequality
To graph the inequality \( v > 146 \):
1. **Draw a number line**: Label it with values that include at least 140 to 160 for reference.
2. **Identify the boundary point**: At \( v = 146 \), make a hollow (open) circle, indicating that 146 is not included in the solution.
3. **Shade the appropriate region**: Since \( v \) is greater than 146, you would shade to the right of the open circle to indicate all the values that are greater than 146.
Here is a visual representation:
```
<---|---|----|----|----|----|----|----|----|----|----|---->
140 141 142 143 144 145 (146) 147 148 149 150 151 152 153 154 155 156
- - - - - - - O - - - - - - - - - - (shaded to the right)
```
The shaded area indicates all the values greater than 146, thus representing the amount of money raised by Mr. Vance's class.