Let's denote the total number of residents surveyed as \( r \).
According to the problem, two-fifths of the residents stated that they like spending their vacation at the beach, and this amounts to 80 residents. We can express this mathematically as:
\[ \frac{2}{5} r = 80 \]
To solve for \( r \), we can multiply both sides of the equation by \( \frac{5}{2} \):
\[ r = 80 \times \frac{5}{2} \]
Calculating the right side:
\[ r = 80 \times 2.5 = 200 \]
Thus, the total number of residents surveyed is \( 200 \).
In summary:
- The equation representing the number of residents surveyed is \( \frac{2}{5} r = 80 \).
- The number of residents surveyed is \( 200 \).