Question

Constructed Response Question
Elizabeth has 8 ounces of chopped vegetables in a mixing bowl. She needs to have a minimum of 50 ounces for a party-sized salad recipe. The measuring cup Elizabeth uses holds 3 ounces.

Write an inequality that can be used to find the number of times, x, that Elizabeth should fill the measuring cup with chopped vegetables in order to follow the recipe. Solve the inequality, and graph the solution set in the space below. Show your work.

Answer 1

To find the number of times, \( x \), that Elizabeth should fill the measuring cup, we can start by setting up the inequality based on the minimum amount of vegetables needed for the salad.

1. **Understand the Problem**:
- Elizabeth currently has 8 ounces of chopped vegetables.
- She needs a total of at least 50 ounces.

2. **Set Up the Inequality**:
- Each time she fills the measuring cup, she adds 3 ounces of vegetables.
- Therefore, after filling the measuring cup \( x \) times, the total amount of vegetables she will have is \( 8 + 3x \).
- We want this amount to be at least 50 ounces:

\[
8 + 3x \geq 50
\]

3. **Solve the Inequality**:
- Start by isolating \( 3x \):

\[
3x \geq 50 - 8
\]
\[
3x \geq 42
\]

- Next, divide both sides by 3:

\[
x \geq \frac{42}{3}
\]
\[
x \geq 14
\]

4. **Conclusion**:
- Elizabeth needs to fill the measuring cup at least 14 times.

### Graph the Solution Set:

To graph the inequality \( x \geq 14 \):

1. **Draw a number line**.
2. **Plot the critical point, 14**.
3. **Since the inequality is greater than or equal to (≥), draw a solid dot at 14** to indicate that 14 is included in the solution.
4. **Shade the line to the right of 14** to indicate that all numbers greater than 14 are also solutions.

### Graph Representation

```
<----|---|---|---|---|---|---|---|---|---|---|---|--->
11 12 13 14 15 16 17 18 19 20 21 22
●=============================>
```

**Note**: The solid dot at 14 represents that 14 is included in the solution, and the shading indicates all values greater than 14 are solutions as well.