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

2/5r=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.

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

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

Answer 1

To find the equation that represents the number of residents surveyed, we know that two-fifths of the total number of respondents \( r \) equals 80 residents who like the beach. This can be expressed as:

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

Now, we can solve for \( r \) to find out how many residents were surveyed. To do this, multiply both sides of the equation by \( \frac{5}{2} \):

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

Calculating that gives:

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

So the total number of residents surveyed is \( 200 \).

The correct response is:

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