https://file.aiquickdraw.com/mathbot/file/1726103614798vj4z9zrv.jpg

The problem in the image states:

Scientists are trying to estimate the fish population in a lake. They catch, tag, and release 200 fish. Later, a new catch shows that 12% of the fish caught are tagged. The task is to estimate the total number of fish in the lake.

### Let's break it down and solve step-by-step:

1. Let **x** represent the total number of fish in the lake.
2. We know 12% of the fish in the lake are tagged. This means that:
   
   \[
   0.12 \times x = 200 \quad \text{(since 200 tagged fish were released)}
   \]

3. To find **x**, we solve for **x** by dividing both sides of the equation by 0.12:

   \[
   x = \frac{200}{0.12}
   \]

4. Calculating the right side:

   \[
   x = 1666.67
   \]

So, the estimated total number of fish in the lake is approximately **1,667**.

Would you like further clarification, or do you have any questions?

### Related questions:
1. What assumptions are made in this type of population estimation?
2. How would the estimate change if only 10% of the fish caught were tagged?
3. What method are the scientists using to estimate the fish population?
4. If the tagging process were repeated, what factors could affect the accuracy of the estimate?
5. How does the concept of proportions apply to this problem?

### Tip: 
When solving population estimation problems like this, remember that the proportion of tagged fish in the sample should be representative of the proportion of tagged fish in the entire population.

Scientists are trying to estimate the fish population in a lake. They catch, tag, and release 200 fish. Later, a new catch shows that 12% of the fish caught are tagged. The task is to estimate the total number of fish in the lake.

Learn how to estimate the fish population in a lake using tagged fish and a proportion-based formula. This problem involves algebraic manipulation and percentage calculations, suitable for Grades 7-9.

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