To determine the number of residents surveyed, we can set up the equation based on the information given:
We know that two-fifths of the respondents liked spending their vacation at the beach, and that number equals 80 residents.
This can be expressed in equation form as:
\[ \frac{2}{5}r = 80 \]
where \( r \) represents the total number of residents surveyed.
To solve for \( r \), we can multiply both sides of the equation by the reciprocal of \(\frac{2}{5}\), which is \(\frac{5}{2}\):
\[ r = 80 \times \frac{5}{2} \]
Calculating this gives:
\[ r = 80 \times 2.5 = 200 \]
So, the total number of residents surveyed is 200.
The correct equation that represents the number of residents surveyed is:
\(\frac{2}{5}r = 80\)
Thus, the complete answer is:
Start Fraction 2 over 5 End Fraction r equals 80 ; 200 residents were surveyed.