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

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

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

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

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

Answer 1

To find the number of residents surveyed, we start with the information given in the problem.

Two-fifths of the respondents like spending their vacation at the beach, and this amount is equal to 80 residents. We can express this relationship with the equation:

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

Where \( r \) is the total number of residents surveyed.

To solve for \( r \), we can rearrange the equation:

1. Multiply both sides by \( \frac{5}{2} \) to isolate \( r \): \[ r = 80 \times \frac{5}{2} \]
2. Calculate that: \[ r = 80 \times 2.5 = 200 \]

Therefore, the equation representing the number of residents surveyed is:

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

And the total number of residents surveyed is:

200 residents.

So, the correct response is:

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