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

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.

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

25r=80
; 32 residents were surveyed.
Start Fraction 2 over 5 End Fraction r equals 80 ; 32 residents were surveyed.
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Answer 1

To find the number of residents surveyed, we can start by interpreting the information given in the problem. We know that two-fifths of the respondents (let's denote the total number of residents surveyed as \( r \)) said they like spending their vacation at the beach, and this number is 80.

This can be written as an equation:

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

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

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

2. Now, divide both sides by \( 2 \): \[ r = 200 \]

Thus, the equation that represents the number of residents surveyed is:

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

And the total number of residents surveyed is 200.

The correct response is:

\(\frac{2}{5} r = 80; 200\) residents were surveyed.