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The problem states:

To fill a bucket with water, two taps were opened. From the first tap, **\( 8 \frac{3}{4} \, \text{l} \)** were obtained, and from the second tap, **\( 5 \frac{5}{6} \, \text{l} \)**. The bucket previously contained **\( \frac{5}{12} \, \text{l} \)** of water. What was the final content of the bucket?

### Steps to solve:

1. Convert the mixed numbers into improper fractions:
   - \( 8 \frac{3}{4} = \frac{35}{4} \)
   - \( 5 \frac{5}{6} = \frac{35}{6} \)

2. Add all the volumes, including the initial amount in the bucket:
   \[
   \text{Total water} = \frac{35}{4} + \frac{35}{6} + \frac{5}{12}
   \]

3. Find the least common denominator (LCD) for 4, 6, and 12. The LCD is 12.

4. Rewrite each fraction with the denominator 12:
   \[
   \frac{35}{4} = \frac{105}{12}, \quad \frac{35}{6} = \frac{70}{12}, \quad \frac{5}{12} = \frac{5}{12}
   \]

5. Add the fractions:
   \[
   \frac{105}{12} + \frac{70}{12} + \frac{5}{12} = \frac{180}{12} = 15 \, \text{liters}
   \]

### Final Answer:
The final amount of water in the bucket is **15 liters**.

Would you like further details on the solution, or do you have any questions?

Here are five questions to expand your understanding:

1. How do you convert a mixed number to an improper fraction?
2. Why is finding the least common denominator important in adding fractions?
3. What other methods could you use to solve the problem of adding fractions?
4. Can you think of real-life situations where adding mixed numbers is useful?
5. How would the problem change if one of the taps provided a negative amount of water?

**Tip:** When working with mixed numbers, always convert them to improper fractions before performing operations like addition or subtraction.

Para llenar una cubeta con agua se abrieron dos llaves. De la primera se obtuvieron 8 3/4 l y de la segunda, 5 5/6 l. Si la cubeta tenía previamente 5/12 l de agua, ¿cuál fue el contenido final de la cubeta?

Learn how to solve a real-life math problem involving the addition of mixed numbers and fractions. This problem involves calculating the final amount of water in a bucket after two taps with different water outputs were opened. Suitable for students in Grades 5-7.

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