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

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.

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

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

Answer 1

To find the number of residents surveyed, we can start with the information provided: two-fifths of the respondents (denoted as \( r \)) equals 80 residents who like spending their vacation at the beach.

We can set up the equation as follows:

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

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

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

Thus, the number of residents surveyed is 200.

The equation that represents the number of residents surveyed is:

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

So the correct option is:

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