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

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

80r=25
; 200 residents were surveyed.

Answer 1

To solve the problem, we start with the information given. We know that two-fifths of the residents surveyed said they like the beach, which equals 80 residents.

We can translate this into an equation:

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

Here, \( r \) represents the total number of residents surveyed.

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

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

Calculating this gives:

\[ r = 80 \times 2.5 = 200 \]

Thus, the total number of residents surveyed is 200.

The correct equation representing the number of residents surveyed is:

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

And the answer is that 200 residents were surveyed.

The correct response is:

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