https://file.aiquickdraw.com/mathbot/file/1726202622433xdt48r9y.jpg

Let's break down the content of the image and solve it step by step.

### Problem Breakdown:

#### 1. **Question b (top):**
   - "Write an equation that represents the amount of money Mrs. Freezle spent if she purchased an ice cream cone with 16 ounces of frozen yogurt."

   **Answer:**
   The equation should express the total cost, where there might be a base cost and a cost per ounce. Let's assume the cost per ounce of frozen yogurt is the same as the rate in the next equation (0.75 dollars per ounce).
   
   The equation can be written as:
   \[
   c = 3 + 0.75 \times 16
   \]
   where:
   - $c$ is the total cost,
   - 3 represents a fixed cost (like a base price for the cone),
   - 0.75 is the cost per ounce,
   - 16 is the number of ounces of frozen yogurt.

   Solving this:
   \[
   c = 3 + 0.75 \times 16 = 3 + 12 = 15
   \]
   So, the total cost is $15.

#### 2. **Suppose Mrs. Freezle writes the equation $18 = 3 + 0.75z$:**
   
   **a. What is the question trying to ask?**
   The equation is likely asking how many ounces of frozen yogurt Mrs. Freezle bought if the total cost was $18. Here, $z$ represents the number of ounces of frozen yogurt.

   **b. How can you answer Mrs. Freezle's question?**
   You can solve this equation by isolating $z$:
   \[
   18 = 3 + 0.75z
   \]
   Subtract 3 from both sides:
   \[
   15 = 0.75z
   \]
   Divide both sides by 0.75:
   \[
   z = \frac{15}{0.75} = 20
   \]
   Therefore, Mrs. Freezle bought 20 ounces of frozen yogurt.

   **Table and Graph:**
   You are asked to complete the table with different values for $z$ (ounces) and calculate the corresponding cost ($c$) using the equation $c = 3 + 0.75z$. Here's how you can fill in the table:

   - For $z = 0$, $c = 3 + 0.75(0) = 3$
   - For $z = 10$, $c = 3 + 0.75(10) = 10.5$
   - For $z = 20$, $c = 3 + 0.75(20) = 18$
   - For $z = 30$, $c = 3 + 0.75(30) = 25.5$

   You can plot these points on the graph to visualize the linear relationship.

---

### Do you have any further questions or would like more details on any part?

Here are five related questions for practice:

1. What would the total cost be if Mrs. Freezle bought 25 ounces of frozen yogurt?
2. How would the equation change if the base cost (3 dollars) increased to 5 dollars?
3. What is the slope of the line in the equation $c = 3 + 0.75z$ and what does it represent?
4. If the total cost was $21, how many ounces of frozen yogurt did Mrs. Freezle buy?
5. How would the graph of the equation change if the cost per ounce increased to $1?

**Tip:** When solving linear equations, always remember to isolate the variable on one side of the equation using basic arithmetic operations like addition, subtraction, multiplication, and division.

Write an equation that represents the amount of money Mrs. Freezle spent if she purchased an ice cream cone with 16 ounces of frozen yogurt.

Learn how to calculate the cost of frozen yogurt based on the number of ounces using the equation c = 3 + 0.75z. This problem involves basic algebra and linear equation solving. Suitable for students in Grades 6-8.

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