Question

A research assistant sent out a survey to n people, hoping to get as many responses back as possible.

If the number of people who did not respond to the survey was 300 less than the number of people
who did respond, what fraction of the people who received the survey did respond?

Answer 1

`(n+300)/(2n)` is the correct answer.

Explanation:

Given that total number of people = n

Let the number of people who responded to the survey = x

Let the number of people who did not respond to the survey = y

`x+y=n ...... (1)`

As per question statement:

The number of people who did not respond to the survey was 300 less than the number of people who did respond.

i.e.
`x-y =300` ...... (2).

We need to solve the equations (1) and (2).

Adding (1) and (2):

`2x=n+300\\\Rightarrow x = (n+300)/(2)`

The fraction of people who received the survey did respond:

`\frac{\text{Number of people who responded}}{\text{Total number of people who received the survey}}\\`

So, the answer is:

`(x)/(n)`

Putting the values of x, we get the answer as:

`(n+300)/(2n)`