prompts/main_prompt.py

Great! Let's dive into each problem type one by one and explore them further.

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📌 **Problem 1: Missing Value Problem**  
**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?"*

### **Solution Strategy:**
1️⃣ **Understand the Scale:**  
   - You know that **2 cm** on the map corresponds to **25 miles** in reality.  
2️⃣ **Set Up a Proportion:**  
   $$
   \frac{2 \,\text{cm}}{25 \,\text{miles}} = \frac{24 \,\text{cm}}{x \,\text{miles}}
   $$  
3️⃣ **Cross-Multiply and Solve:**  
   $$
   2x = 24 \times 25
   $$  
4️⃣ **Calculate:**  
   $$
   x = \frac{24 \times 25}{2} = 300 \text{ miles}
   $$  
**Conclusion:** *24 cm on the map represents **300 miles**.*

---

📌 **Problem 2: Numerical Comparison Problem**  
**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?"*

### **Solution Strategy:**
1️⃣ **Calculate the Unit Price for Each:**  
   $$
   \text{Cost per pencil for Ali} = \frac{\$3.50}{10} = \$0.35
   $$  
   $$
   \text{Cost per pencil for Ahmet} = \frac{\$1.80}{5} = \$0.36
   $$  
2️⃣ **Compare the Unit Prices:**  
   - **Ali pays \$0.35 per pencil**  
   - **Ahmet pays \$0.36 per pencil**  
3️⃣ **Conclusion:** *Ali got the better deal because he paid **less per pencil**.*

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📌 **Problem 3: Qualitative Reasoning Problem**  
**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?"*

### **Solution Strategy:**
1️⃣ **Understand the Change in Ratios:**  
   - Today, the **amount of red paint has increased**, while **white paint remains constant**.  
2️⃣ **Qualitative Analysis:**  
   - Since **the proportion of red paint has increased**, today's mixture will be **more red (darker)** compared to yesterday.

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💬 **Discussion:**  
✔ **Which problem do you want to start with?**  
✔ **What is the first strategy that comes to your mind for solving it?**  
✔ **Would you like a hint before starting?**  

Feel free to ask for guidance or clarification on any of the problems!