Let's say a school is organizing a fund raiser to buy new sports equipment. The goal is to raise $500. You and your friend decide to sell homemade cookies and lemonade. Each cookie sells for $2 and each cup of lemonade sells for $1.50. While doing this, you and your friends want to figure out how many cookies and cups of lemonade you will need to sell to get get the fund raising goal. The goal is to reach $500.00. Please solve this problem using equations and inequalities. Please answer this question in a way that a 6th grader will understand. 

Let's break this down step by step so it's easy to understand.

The goal is to raise **$500** by selling **cookies** and **lemonade**. Here’s what we know:

- Each **cookie** sells for **$2**.
- Each **cup of lemonade** sells for **$1.50**.

You and your friend need to sell enough cookies and lemonade so that when you add up the money, it equals **$500** or more.

### Step 1: Defining the Variables
Let’s use two letters to represent how many cookies and cups of lemonade you sell:
- Let **C** be the number of cookies you sell.
- Let **L** be the number of cups of lemonade you sell.

### Step 2: Write the Equation for the Total Money
The money you earn from selling cookies and lemonade will add up to help you reach your goal. Here’s how:

- Each cookie is **$2**, so the money from cookies is **2 × C** (or just **2C**).
- Each cup of lemonade is **$1.50**, so the money from lemonade is **1.5 × L** (or just **1.5L**).

The total money raised must be at least $500, so we write the equation (or inequality):

\[
2C + 1.5L \geq 500
\]

This means the total money from cookies and lemonade should be **greater than or equal to** $500.

### Step 3: Think About Possible Combinations
Now that we have the equation, let's explore how many cookies and lemonade cups you could sell to reach the goal.

Here are some examples to make this clearer:

1. **If you sell only cookies**:
   - To raise $500 by only selling cookies, divide $500 by $2 per cookie.
   \[
   C = \frac{500}{2} = 250
   \]
   You would need to sell **250 cookies** to reach $500 if you don’t sell any lemonade.

2. **If you sell only lemonade**:
   - To raise $500 by only selling lemonade, divide $500 by $1.50 per cup.
   \[
   L = \frac{500}{1.5} \approx 333.33
   \]
   You would need to sell about **334 cups of lemonade** to reach $500 if you don’t sell any cookies.

### Step 4: Selling Both Cookies and Lemonade
In most cases, you’ll probably sell **some cookies** and **some lemonade**. Let's say you sell 100 cookies, then the money raised from cookies is:
\[
2 \times 100 = 200
\]
Now, you need to raise the rest of the money, $500 - $200 = $300, by selling lemonade. To find out how many cups of lemonade that would take:
\[
L = \frac{300}{1.5} = 200
\]
So, if you sell **100 cookies** and **200 cups of lemonade**, you’ll reach your goal of $500.

### Conclusion
You can sell different combinations of cookies and lemonade to reach your $500 goal. The inequality **2C + 1.5L ≥ 500** helps you figure out how much of each you need to sell.

Would you like to try some other combinations, or do you have any questions?

---

Here are 5 follow-up questions you might find interesting:
1. How many cookies and lemonade cups should you sell if you want to raise **exactly** $600?
2. What if you sell 50 cookies, how many lemonade cups would you need to sell?
3. What if each cookie was sold for $2.50 instead? How would that change the equation?
4. If you have a limited time to sell and can only sell 200 items in total, what are some combinations of cookies and lemonade you could sell to raise at least $500?
5. What if your goal is $800? How would the equation change?

**Tip:** Always double-check your math to make sure your combination of cookies and lemonade adds up to the goal!

Let's say a school is organizing a fund raiser to buy new sports equipment. The goal is to raise $500. You and your friend decide to sell homemade cookies and lemonade. Each cookie sells for $2 and each cup of lemonade sells for $1.50. While doing this, you and your friends want to figure out how many cookies and cups of lemonade you will need to sell to get the fund raising goal. The goal is to reach $500.00. Please solve this problem using equations and inequalities. Please answer this question in a way that a 6th grader will understand.

Learn how to solve a real-life fundraising problem where you sell cookies and lemonade to reach a goal of $500. This solution introduces algebraic concepts, including linear equations and inequalities. Perfect for 6th graders learning how to apply math to everyday scenarios.

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