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

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

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

52r=80
5
2
𝑟
=
80
; 200 residents were surveyed.

Answer 1

To find the number of residents surveyed, we start with the information given:

- Two-fifths of the respondents (the residents surveyed) said they like spending their vacation at the beach.
- This number (two-fifths of the total respondents) equals 80 residents.

Let's express that relationship as an equation.

Let \( r \) be the total number of residents surveyed. According to the problem:
\[
\frac{2}{5} r = 80
\]

Now, we can solve for \( r \):
1. Multiply both sides of the equation by \( 5 \):
\[
2r = 80 \times 5
\]
\[
2r = 400
\]

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

So, the equation that represents the number of residents surveyed is:
\[
\frac{2}{5} r = 80
\]
And the total number of residents surveyed is \( 200 \).

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