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

Question

Responses

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

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

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

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

Answer 1

To solve the problem, we need to set up an equation based on the information provided. We know that two-fifths of the total number of residents surveyed (denoted as \( r \)) said they like the beach, and this number equals 80 residents.

We can represent this mathematically as:

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

Now, we can solve for \( r \):

1. Multiply both sides by \( 5 \) to eliminate the fraction:

\[ 2r = 80 \times 5 \]

\[ 2r = 400 \]

2. Now, divide both sides by \( 2 \):

\[ r = \frac{400}{2} \]

\[ r = 200 \]

Thus, the total number of residents surveyed is \( 200 \).

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

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

And the total number of residents surveyed is \( 200 \).

So the correct option is:

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