To find out how many residents were surveyed, we first interpret the information given.
We know that two-fifths of the respondents reported liking the beach, and this corresponds to 80 residents. We can set up the following equation:
\[ \frac{2}{5} \times r = 80 \]
where \( r \) represents the total number of residents surveyed.
To solve for \( r \), we can multiply both sides of the equation by \( \frac{5}{2} \) to isolate \( r \):
\[ r = 80 \times \frac{5}{2} \]
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:
\[ \frac{2}{5} \times r = 80 \]
And the total number of residents surveyed is \( r = 200 \).