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?(1 point)
Responses

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

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

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

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

Answer 1

To find the correct equation and the number of residents surveyed, we know that two-fifths of the respondents (r) equals 80 residents:

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

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

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

Calculating that:

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

So, the equation that represents the number of residents surveyed is:

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

And the total number of residents surveyed is:

\[ 200 \text{ residents.} \]

Therefore, the correct response is:

\(\frac{2}{5} r = 80; 200 \text{ residents were surveyed.}\)