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

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

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

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

Answer 1

To set up the equation, we know that two-fifths of the total number of residents surveyed \( r \) is equal to 80 residents who prefer the beach. We can express this as:

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

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

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

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

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

And the total number of residents surveyed is 200 residents.