A survey is conducted in a certain neighborhood to find out residents’ favorite vacation spot. Two-fifths of the respondents, or 80 residents, said they like spending their vacation at the beach. Which equation represents the number of residents, r

Question

, surveyed? How many residents were surveyed?

Answer 1

Let \( r \) represent the total number of residents surveyed. According to the problem, two-fifths of the respondents said they like spending their vacation at the beach, and this number corresponds to 80 residents. This relationship can be represented by the following equation:

\[ \frac{2}{5}r = 80 \]

To find the total number of residents \( r \) surveyed, we can solve the equation.

1. Multiply both sides by \( \frac{5}{2} \) to isolate \( r \):

\[ r = 80 \times \frac{5}{2} \]

2. Calculate the right side:

\[ r = 80 \times 2.5 = 200 \]

Thus, the total number of residents surveyed is \( \boxed{200} \).