### 🚀 MAIN PROMPT ###
MAIN_PROMPT = """
### **Module 3: Proportional Reasoning Problem Types**  
#### **Task Introduction**  
"Welcome to this module on proportional reasoning problem types!  
Your task is to explore three different problem types foundational to proportional reasoning:  
1️⃣ **Missing Value Problems**  
2️⃣ **Numerical Comparison Problems**  
3️⃣ **Qualitative Reasoning Problems**  
You will solve and compare these problems, **identify their characteristics**, and finally **create your own problems** for each type.  
💡 **Throughout this module, I will guide you step by step.**  
💡 **You will be encouraged to explain your reasoning.**  
💡 **If you’re unsure, I will provide hints rather than giving direct answers.**  
🚀 **Let’s get started! Solve each problem and compare them by analyzing your solution process.**"  

---
### **🚀 Solve the Following Three Problems**  
📌 **Problem 1: Missing Value Problem**  
*"The scale on a map is **2 cm represents 25 miles**. If a given measurement on the map is **24 cm**, how many miles are represented?"*  

📌 **Problem 2: Numerical Comparison Problem**  
*"Ali and Ahmet purchased pencils. Ali bought **10 pencils for $3.50**, and Ahmet purchased **5 pencils for $1.80**. Who got the better deal?"*  

📌 **Problem 3: Qualitative Reasoning Problem**  
*"Kim is mixing paint. Yesterday, she combined **red and white paint** in a certain ratio. Today, she used **more red paint** but kept the **same amount of white paint**. How will today’s mixture compare to yesterday’s in color?"*  
"""

### 🚀 PROBLEM SOLUTIONS ###
PROBLEM_SOLUTIONS_PROMPT = """
### **🚀 Step-by-Step Solutions**
#### **Problem 1: Missing Value Problem**  
We set up the proportion:  
$$
\frac{2 \text{ cm}}{25 \text{ miles}} = \frac{24 \text{ cm}}{x \text{ miles}}
$$  
Cross-multiply:  
$$
2x = 24 \times 25
$$  
Solve for \( x \):  
$$
x = \frac{600}{2} = 300
$$  
**Conclusion:** *24 cm represents **300 miles**.*

---
#### **Problem 2: Numerical Comparison Problem**  
**Calculate unit prices:**  
$$
\text{Price per pencil (Ali)} = \frac{\$3.50}{10} = \$0.35
$$  
$$
\text{Price per pencil (Ahmet)} = \frac{\$1.80}{5} = \$0.36
$$  
**Comparison:**  
- Ali: **\$0.35** per pencil  
- Ahmet: **\$0.36** per pencil  

**Conclusion:** *Ali got the better deal because he paid **less per pencil**.*

---
#### **Problem 3: Qualitative Reasoning Problem**  
🔹 **Given Situation:**  
- Yesterday: **Ratio of red to white paint**  
- Today: **More red, same white**

🔹 **Reasoning:**  
- Since the amount of **white paint stays the same** but **more red paint is added**, the **red-to-white ratio increases**.
- This means today’s mixture is **darker (more red)** than yesterday’s.

🔹 **Conclusion:**  
- *The new paint mixture has a **stronger red color** than before.*
"""