Question

lizabeth 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 with chopped vegetables, we can start by forming an inequality.

1. **Identify the variables:**
The current amount of chopped vegetables is 8 ounces, and each fill of the measuring cup adds 3 ounces to that amount. Therefore, after filling the cup \(x\) times, the total amount of chopped vegetables will be:
\[
8 + 3x
\]

2. **Set up the inequality:**
Elizabeth needs a minimum of 50 ounces. Therefore, we can write the inequality as:
\[
8 + 3x \geq 50
\]

3. **Solve the inequality:**
To solve for \(x\), we first subtract 8 from both sides:
\[
3x \geq 50 - 8
\]
\[
3x \geq 42
\]

Next, divide both sides by 3:
\[
x \geq \frac{42}{3}
\]
\[
x \geq 14
\]

4. **Interpret the result:**
This means that Elizabeth needs to fill the measuring cup at least 14 times to have the required 50 ounces of chopped vegetables.

5. **Graph the solution set:**
The solution \(x \geq 14\) can be represented on a number line:

\[
\text{Number line:}
\]
\[
\text{---|---|---|---|---|---|---|---|---|---|---|---}
10 11 12 13 14 15 16 17 18 19 20
\]
- Draw a solid dot at 14 to indicate that it is included in the solution set.
- Shade to the right of 14 to indicate all values greater than or equal to 14.

The complete solution is \( x \geq 14 \).