1. **State the problem:** We have a club with $x$ adults. Out of these, some are over 30 years old. 2. **Given data:** - 20 adults are chosen at random. - 8 of these 20 adults are over 30 years old. 3. **Goal:** Estimate the value of $n$, which represents the number of adults over 30 in the entire club. 4. **Approach:** We use the proportion of adults over 30 in the sample to estimate the total number over 30 in the club. 5. **Calculate the proportion in the sample:** $$\frac{8}{20} = \frac{2}{5}$$ 6. **Set up the proportion for the whole club:** If $n$ is the number of adults over 30 in the club, and $x$ is the total number of adults, then: $$\frac{n}{x} = \frac{2}{5}$$ 7. **Solve for $n$:** $$n = x \times \frac{2}{5}$$ 8. **Interpretation:** The estimate for $n$ is $\frac{2}{5}$ of the total number of adults $x$ in the club. **Final answer:** $$n = \frac{2}{5} x$$