To find the equation that represents the number of residents surveyed (r), we know that two-fifths of the respondents (r) equals 80 residents who like spending their vacation at the beach.
We can set up the equation as follows:
\[ \frac{2}{5} r = 80 \]
Next, to solve for r, we multiply both sides by the reciprocal of \(\frac{2}{5}\), which is \(\frac{5}{2}\):
\[ r = 80 \cdot \frac{5}{2} \]
Calculating this gives:
\[ r = 80 \cdot 2.5 = 200 \]
So, the equation is \(\frac{2}{5} r = 80\) and the total number of residents surveyed is 200.
The correct response is:
\(\frac{2}{5} r = 80\); 200 residents were surveyed.