Question

A survey is conducted in a certain neighborhood to find residents' favorite vacation spot. Two-fiths of the respondents, or 80 residents, said they liked spending their vacation at the beach. Which equation represents the number of residents, r , surveyed? How many residents were surveyed?

Answer 1

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

Answer 2

We know that two-fifths of the respondents said they liked spending their vacation at the beach. This can be represented mathematically as:

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

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

To find the number of residents surveyed, we can solve this equation 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 to solve for \( r \):

\[
r = \frac{400}{2}
\]
\[
r = 200
\]

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

The equation that represents the situation is:

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

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

Answer 3

That's correct! You've accurately summarized the information.

To reiterate:

- The equation that represents the number of residents surveyed is \(\frac{2}{5}r = 80\).
- Solving this equation gives you \(r = 200\), meaning 200 residents were surveyed in total.

If you have any more questions or need further assistance, feel free to ask!