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The problem described is a typical capture-recapture estimation method to determine the total population of seals. Here's the process to estimate the total number of seals using the given information:

### Given:
- 35 seals were initially tagged.
- In a later sample, 14% of the seals had tags.

Let's assume the total population of seals is \( N \).

Using the capture-recapture formula:

\[
\frac{\text{Number of tagged seals}}{\text{Total population}} = \frac{\text{Percentage of tagged seals in sample}}{100}
\]

We know:
- Tagged seals = 35.
- Percentage of tagged seals in the sample = 14%.

Thus, the formula becomes:

\[
\frac{35}{N} = \frac{14}{100}
\]

Now, solving for \( N \):

\[
N = \frac{35 \times 100}{14}
\]

Let me calculate that for you.The estimated total number of seals in the area is 250.

Do you want any further details or have additional questions?

Here are some related questions to expand on this topic:
1. How would the estimate change if the percentage of tagged seals in the sample was 10%?
2. What assumptions are made in the capture-recapture method for population estimation?
3. How can we increase the accuracy of the population estimate using this method?
4. What is the mathematical explanation behind the capture-recapture technique?
5. How would the estimate differ if a larger number of seals were tagged initially?

**Tip:** When applying the capture-recapture method, ensure that the tagged animals mix evenly with the untagged population between samplings.

A team of biologists tagged 35 seals off the coast of an island. Later they captured a sample of seals from the same area and found that 14% of them had tags. Use this information to estimate the total number of seals in the area.

Learn how to estimate the total number of seals in an area using the capture-recapture method. This problem involves calculating the population of seals using proportionality, where 35 seals were tagged and 14% of them were found in a later sample. Suitable for students in Grades 9-12.

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