https://file.aiquickdraw.com/mathbot/file/1730093899319vylli8be.jpg

Let's go through each part of this exercise.

### Question 7
"Write down a number greater than -8 but smaller than 2."

Examples of numbers that satisfy this condition include:
- -7, -5, 0, 1, etc.

Any number in the range \(-8 < x < 2\) would be correct.

---

### Question 8
We have a water container with water being pumped in and leaking out.

#### Part (a)
We need to represent the rate of water being pumped in and leaking out using directed numbers:
- **Water being pumped in**: 2 L per minute (since it's being added, it would be represented as \(+2\))
- **Water leaking out**: 0.15 L per minute (since it's being removed, it would be represented as \(-0.15\))

Thus, the directed numbers are:
\[
+2 \, \text{ and } \, -0.15
\]

#### Part (b)
We need to find the amount of water in the container after half an hour (30 minutes).

Since the net gain in water per minute is:
\[
2 - 0.15 = 1.85 \, \text{L per minute}
\]

Over 30 minutes, the total amount of water in the container is:
\[
1.85 \times 30 = 55.5 \, \text{L}
\]

### Final Answers
- **(a)** \( +2 \) and \( -0.15 \)
- **(b)** 55.5 L

Would you like further details or have any questions about these calculations?

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Here are five related questions to deepen your understanding:
1. What if the leak rate increased to 0.5 L per minute? How would that change the total water in the container after half an hour?
2. How would the total amount of water change if the pumping rate was decreased to 1.5 L per minute?
3. Can you write a formula for the amount of water after \( t \) minutes given a specific pump rate and leak rate?
4. What is the net change in water if the pumping and leaking rates are equal?
5. How long would it take to fill the container to 100 L if the net increase per minute remains at 1.85 L?

**Tip:** Always double-check units and make sure they align throughout your calculations to avoid errors.

Write down a number greater than -8 but smaller than 2. It is known that 2 L of water is pumped into an empty container every minute. Suppose there is 0.15 L of water leaking from a small hole at the bottom of the container every minute. (a) Use directed numbers to represent the amount of water leaking and being pumped in one minute respectively. (b) Find the amount of water in the container after pumping for half an hour.

Learn how to calculate the net water in a container with a constant pump and leak rate. This problem involves using directed numbers to represent rates and finding the total water after 30 minutes. Suitable for students in Grades 6-8.

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