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Let's solve this step by step.

1. **Initial Condition:**
   - The number of tulips initially is \( 2n + 1 \).
   - The number of daffodils is 12.

2. **After Adding Tulips:**
   - 3 more tulips are added, making the new total of tulips \( (2n + 1) + 3 = 2n + 4 \).

3. **New Ratio Condition:**
   - The new ratio of tulips to daffodils is 11:6.
   - This gives the equation:
     \[
     \frac{2n + 4}{12} = \frac{11}{6}.
     \]

4. **Solve the Equation:**
   - Cross-multiply to solve for \( n \):
     \[
     6(2n + 4) = 11 \times 12.
     \]
   - This simplifies to:
     \[
     12n + 24 = 132.
     \]
   - Subtract 24 from both sides:
     \[
     12n = 108.
     \]
   - Divide by 12:
     \[
     n = 9.
     \]

Therefore, the value of \( n \) is 9.

Would you like a more detailed explanation, or do you have any questions? 

Here are some related questions for further practice:
1. What would be the new ratio if 5 more tulips were added instead of 3?
2. If the ratio of tulips to daffodils was instead 5:3 after adding 3 tulips, what would be the value of \( n \)?
3. How many tulips and daffodils are there in total when \( n = 9 \)?
4. What happens to the ratio if 2 daffodils are removed from the flowerbed?
5. If initially there were twice as many tulips as daffodils, what equation would you use to find \( n \)?

**Tip:** When solving ratio problems, setting up an equation that equates the two ratios is crucial for finding the unknown value.

To start with, there were 2n + 1 tulips and 12 daffodils in a flowerbed. 3 more tulips were then added to the flowerbed, and the ratio of tulips to daffodils is now 11:6. Calculate the value of n.

Learn how to solve a ratio problem involving tulips and daffodils. Given that the initial number of tulips was 2n + 1 and 3 more tulips were added, making the tulip to daffodil ratio 11:6, this solution walks through solving for n step by step. Suitable for students in Grades 8-10.

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