https://file.aiquickdraw.com/mathbot/file/1725304627657qszqm9xo.jpg

To solve this problem, let's analyze the given information from the image.

### Problem Breakdown:

1. **Initial Information:**
   - A tank and a pail together contain a total of **8,346 mL** of water.
   - After some water is poured from the tank into the pail, the tank has **3,314 mL** left.

2. **Goal:**
   - Determine the amount of water in the pail in the end.
   - Determine how much water was initially in the pail.
   - Calculate how much water was initially in the tank.

### Steps to Solve:

1. **Calculate the amount of water transferred to the pail:**

   Since the tank initially contained 8,346 mL of water and now contains 3,314 mL:

   \[
   \text{Water transferred to pail} = 8,346 \, \text{mL} - 3,314 \, \text{mL}
   \]

   \[
   = 5,032 \, \text{mL}
   \]

2. **Determine the final amount of water in the pail:**

   If we denote the initial amount of water in the pail as \( P \), the final amount in the pail will be the initial amount plus the water transferred from the tank:

   \[
   \text{Final amount in pail} = P + 5,032 \, \text{mL}
   \]

3. **Calculate the initial amounts of water:**

   The total initial amount of water in the tank and pail together was 8,346 mL. This includes the initial water in the tank \( T \) and the initial water in the pail \( P \):

   \[
   T + P = 8,346 \, \text{mL}
   \]

   After pouring, the tank has 3,314 mL, so:

   \[
   P + 5,032 = 8,346 - 3,314
   \]

   \[
   P + 5,032 = 5,032 \, \text{mL} \implies P = 0 \, \text{mL}
   \]

   Hence, there was no water in the pail initially.

4. **Initial water in the tank:**

   Since there was no water initially in the pail, the initial amount of water in the tank is the total initial amount:

   \[
   T = 8,346 \, \text{mL}
   \]

### Summary:

- **Initial amount of water in the pail:** \(0 \, \text{mL}\)
- **Initial amount of water in the tank:** \(8,346 \, \text{mL}\)
- **Amount of water transferred to the pail:** \(5,032 \, \text{mL}\)
- **Final amount of water in the pail:** \(5,032 \, \text{mL}\)

Would you like more details or have any questions? 

Here are 5 related questions for further practice:

1. If the tank initially had 10,000 mL and the pail had 2,000 mL, how much water would be left in the tank after transferring 4,000 mL to the pail?
2. How much water would need to be transferred if the pail initially had 1,000 mL and needed to be filled to 6,000 mL?
3. If a different pail could hold 8,000 mL and the tank started with 12,000 mL, how much water would be left in the tank after filling the pail completely?
4. How would the amounts change if the total amount of water was 15,000 mL instead of 8,346 mL?
5. What would happen if instead of transferring water from the tank to the pail, the process was reversed?

**Tip:** Always check the units (mL in this case) to make sure all parts of the problem are using the same measurements.

Learn how to solve a mathematical problem involving the transfer of water between a tank and a pail. This problem includes detailed steps to determine initial water amounts, transferred water, and final amounts in the pail. Suitable for students in Grades 7-9.

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