https://file.aiquickdraw.com/mathbot/file/17278044353669d9k0img.jpg

Let's break down the problem from the image and solve it step-by-step.

**Given:**
- Max earned $20 by selling 10 baked goods.
- He sold two types of items: cookies for $1.25 each and brownies for $2.50 each.
- We are tasked with finding how many cookies and brownies Max sold by solving a system of equations.

### Step 1: Define Variables
Let:
- $ x $ be the number of cookies sold.
- $ y $ be the number of brownies sold.

### Step 2: Set up the system of equations
From the problem, we have the following information:
1. The total number of items sold is 10:
   \[
   x + y = 10 \quad \text{(Equation 1)}
   \]
2. The total amount earned from selling the cookies and brownies is $20:
   \[
   1.25x + 2.50y = 20 \quad \text{(Equation 2)}
   \]

### Step 3: Solve the system of equations
We can solve this system by substitution or elimination. I'll use substitution.

From **Equation 1**, solve for $ y $:
\[
y = 10 - x
\]

Substitute this into **Equation 2**:
\[
1.25x + 2.50(10 - x) = 20
\]
Expand the equation:
\[
1.25x + 25 - 2.50x = 20
\]
Combine like terms:
\[
-1.25x + 25 = 20
\]
Subtract 25 from both sides:
\[
-1.25x = -5
\]
Solve for $ x $:
\[
x = 4
\]

### Step 4: Solve for $ y $
Substitute $ x = 4 $ back into **Equation 1**:
\[
4 + y = 10
\]
\[
y = 6
\]

### Conclusion:
Max sold **4 cookies and 6 brownies**.

So the correct answer is:
\[
\boxed{C}
\]

Let me know if you want more details or have any questions! Here are some follow-up questions that build on this:

1. How would the equations change if the price of cookies was increased to $2.00?
2. What if Max sold 15 items and made $30? How would you approach that?
3. How could we solve this using the elimination method?
4. What if the total earnings were $22 instead of $20?
5. Can you use a graph to represent this system of equations?

**Tip:** Always verify your final answer by plugging the values back into the original equations to ensure both are satisfied!

Max earned $20 when he sold 10 baked goods at the school bake sale. He sold only two types of items, cookies for $1.25 each and brownies for $2.50 each. Write and solve a system of equations to determine how many cookies and brownies Max sold at the bake sale.

Learn how to solve a system of equations to determine how many cookies and brownies Max sold at a bake sale. This math problem involves setting up two equations, solving for the unknowns, and applying algebraic concepts. Suitable for students in Grades 7-9.

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