Question

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
𝑟
, surveyed? How many residents were surveyed?(1 point)
Responses

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

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

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

80r=25
80
𝑟
=
2
5
; 200 residents were surveyed.

Answer 1

To solve the problem, we start with the information given: two-fifths of the respondents, or 80 residents, like spending their vacation at the beach.

This can be expressed mathematically. If \( r \) represents the total number of residents surveyed, then two-fifths of \( r \) can be written as:

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

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

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

So, the total number of residents surveyed is 200.

Now, looking at the provided options, the correct equation that represents the relationship is:

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

Thus, the correct choice is:

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