The ratio of water between fresh fruit and dry fruit is 7:2. If 400 kg of dry fruit contains 50 kg of water, how much water will an equal quantity of fresh fruit contain?

Given the problem:

- The ratio of water in fresh fruit to dry fruit is 7:2.
- 400 kg of dry fruit contains 50 kg of water.

### Step-by-Step Breakdown:

1. **Determine the amount of dry matter in 400 kg of dry fruit:**

   Since 50 kg of the 400 kg is water, the dry matter is:
   \[
   400 \, \text{kg} - 50 \, \text{kg} = 350 \, \text{kg}.
   \]

2. **Recognize the dry matter stays the same:**

   The dry matter content in both fresh and dry fruit is the same because drying only removes water, not dry matter. So, the fresh fruit also has 350 kg of dry matter.

3. **Find the total mass of the fresh fruit:**

   In the fresh fruit, the water-to-dry matter ratio is given as 7:2. This means for every 9 parts (7 parts water and 2 parts dry matter), 2 parts are dry matter.

   The dry matter is 2 parts out of 9, so the total mass of the fresh fruit, \( M \), satisfies:
   \[
   \frac{2}{9} \times M = 350 \, \text{kg}.
   \]
   Solving for \( M \):
   \[
   M = \frac{350 \times 9}{2} = 1575 \, \text{kg}.
   \]

4. **Calculate the water content in the fresh fruit:**

   Since 7 parts of the fresh fruit’s total weight is water, the amount of water in 1575 kg of fresh fruit is:
   \[
   \frac{7}{9} \times 1575 = 1225 \, \text{kg}.
   \]

### Final Answer:
The fresh fruit will contain **1225 kg of water**.

Would you like further details on any of these steps? Here are 5 related questions:

1. What happens to the ratio of water when fruit is dried?
2. How would the problem change if the dry fruit had a different water content?
3. Can you apply this method to calculate other fruit or food transformations?
4. Why is the total dry matter conserved in both fresh and dry fruit?
5. What percentage of the fresh fruit's mass is water?

**Tip:** When solving ratio problems, remember that the total number of parts helps relate different portions like water and dry matter.

This guide provides a step-by-step solution to calculate how much water is in fresh fruit when given the ratio of water to dry matter in fresh and dry fruit. Learn about the use of ratios and proportions with practical examples, perfect for students in Grades 8-10.

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