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

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

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

2/5 r=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 number of residents surveyed, \( r \), given that two-fifths of the respondents (which is \( \frac{2}{5} \) of the total) equals 80 residents, we can set up the equation:

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

Now let's solve for \( r \):

1. Multiply both sides by 5 to eliminate the fraction: \[ 2r = 80 \times 5 \] \[ 2r = 400 \]

2. Now, divide both sides by 2: \[ r = \frac{400}{2} \] \[ r = 200 \]

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

Thus, the answer is: \[ \frac{2}{5} r = 80; , 200 \text{ residents were surveyed.} \]