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

25r=80; 32 residents were surveyed.
Start Fraction 2 over 5 End Fraction r equals 80 ; 32 residents were surveyed.

52r=80; 200 residents were surveyed.
Start Fraction 5 over 2 End Fraction r equals 80 ; 200 residents were surveyed.

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

80r=25; 200 residents were surveyed.

Answer 1

To find the equation that represents the number of residents \( r \) surveyed and the total number of residents surveyed, we start with the information provided:

Two-fifths of the respondents said they like spending their vacation at the beach, and this is equal to 80 residents.

We can express this relationship mathematically as:

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

Now, to solve for \( r \), we can multiply both sides of the equation by the reciprocal of \(\frac{2}{5}\), which is \(\frac{5}{2}\):

\[ r = 80 \times \frac{5}{2} = 80 \times 2.5 = 200 \]

Thus, the number of residents surveyed is \( 200 \).

The correct equation is \(\frac{2}{5} r = 80\), and the total number of residents surveyed is \( 200 \).

So the correct response is: Start Fraction 2 over 5 End Fraction r equals 80; 200 residents were surveyed.