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 , surveyed? How many residents were surveyed?(1 point)

Question

Responses

80r=25; 200 residents were surveyed.
80 r equals Start Fraction 2 over 5 End Fraction ; 200 residents were surveyed.

2/5r=80; 200 residents were surveyed.
Start Fraction 2 over 5 End Fraction r equals 80 ; 200 residents were surveyed.

2/5r=80; 32 residents were surveyed.
Start Fraction 2 over 5 End Fraction r equals 80 ; 32 residents were surveyed.

5/2r=80; 200 residents were surveyed.

Answer 1

To determine the correct equation and the number of residents surveyed, we can start with the information given in the problem. We know that two-fifths of the respondents said they like spending their vacation at the beach, and that corresponds to 80 residents.

Let \( r \) be the total number of residents surveyed. According to the problem:

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

This equation represents that two-fifths of the total residents surveyed equals 80.

To find \( r \), we can solve for \( r \) by multiplying both sides of the equation by \( \frac{5}{2} \):

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

Calculating this results in:

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

Thus, the total number of residents surveyed is 200.

The correct equation is

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

and the number of residents surveyed is 200.

So the correct response is:

2/5r=80; 200 residents were surveyed.