To determine the number of residents surveyed, we know that \( \frac{2}{5} \) of the respondents said they like spending their vacation at the beach, which equals 80 residents.
We can set up the equation based on this information. Let \( r \) be the total number of residents surveyed. According to the problem, we have:
\[ \frac{2}{5}r = 80 \]
This equation shows that 2/5 of the total residents surveyed (r) equals 80.
Now we can solve for \( r \):
- Multiply both sides of the equation by 5 to eliminate the fraction:
\[ 2r = 80 \times 5 \] \[ 2r = 400 \]
- Now, divide both sides by 2:
\[ r = \frac{400}{2} \] \[ r = 200 \]
So, the total number of residents surveyed is 200.
Now, looking at the options provided:
- A. \(80r = \frac{2}{5}\), 200 residents were surveyed (incorrect format)
- B. \(\frac{5}{2}r = 80\), 200 residents were surveyed (incorrect equation)
- C. \(\frac{2}{5}r = 80\), 32 residents were surveyed (incorrect total)
- D. \(\frac{2}{5}r = 200\) residents were surveyed (incorrect equation)
The correct equation is not directly among the options, but the original equation derived from the problem is \(\frac{2}{5}r = 80\) which indicates that \( r = 200 \). Therefore, the best interpretation is D, as the original statement aligns with the representation given in choice C but emphasizes that the total elicited in the question reaffirms \(r\) to be 200.
2 answers