To find the concentration of the new sugar solution, we will calculate the amount of sugar in each solution and then find the concentration in the total mixture.

1. Amount of sugar in 2 liters of 34% solution: \text{Sugar in 34% solution} = 2 \, \text{L} \times \frac{34}{100} = 0.68 \, \text{L of sugar}

2. Amount of sugar in 9 liters of 56% solution: \text{Sugar in 56% solution} = 9 \, \text{L} \times \frac{56}{100} = 5.04 \, \text{L of sugar}

3. Total amount of sugar in the mixture: $\text{Total sugar} = 0.68 \, \text{L} + 5.04 \, \text{L} = 5.72 \, \text{L of sugar}$

4. Total volume of the mixture: $\text{Total volume} = 2 \, \text{L} + 9 \, \text{L} = 11 \, \text{L}$

5. Concentration of the new mixture: $\text{Concentration} = \frac{\text{Total sugar}}{\text{Total volume}} \times 100 = \frac{5.72}{11} \times 100 \approx 52$

Therefore, the concentration of the new sugar solution is approximately 52%.

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. How would the concentration change if more of the 34% solution was added?
2. How do you find the concentration when solutions of unequal volumes are mixed?
3. What happens to the concentration if both solutions had the same percentage?
4. Can this method be applied to any concentration mixture problems?
5. How would the process differ if one solution was a solid, not a liquid?

Tip: When mixing solutions, the key is balancing the total amount of solute across the total volume.