Question
the local library has 4,250 library card holders. The library sends out a survey to every fifth library card holder. If all of the surveyed recipients respond, what percent of the total population has been surveyed
Answers
GPT-4o mini
To find out what percent of the total library card holders has been surveyed, we start by determining how many card holders were surveyed. Given that there are 4,250 library card holders and the library surveys every fifth card holder, we can calculate the number of surveyed card holders as follows:
\[
\text{Number of surveyed card holders} = \frac{4,250}{5} = 850
\]
Next, we need to find the percentage of library card holders who were surveyed. The formula for calculating the percentage is:
\[
\text{Percentage} = \left( \frac{\text{Number surveyed}}{\text{Total population}} \right) \times 100
\]
Substituting the values we have:
\[
\text{Percentage} = \left( \frac{850}{4,250} \right) \times 100
\]
Calculating this gives:
\[
\text{Percentage} = \left( \frac{850}{4,250} \right) \times 100 = 0.2 \times 100 = 20\%
\]
Thus, **20%** of the total population of library card holders has been surveyed.
\[
\text{Number of surveyed card holders} = \frac{4,250}{5} = 850
\]
Next, we need to find the percentage of library card holders who were surveyed. The formula for calculating the percentage is:
\[
\text{Percentage} = \left( \frac{\text{Number surveyed}}{\text{Total population}} \right) \times 100
\]
Substituting the values we have:
\[
\text{Percentage} = \left( \frac{850}{4,250} \right) \times 100
\]
Calculating this gives:
\[
\text{Percentage} = \left( \frac{850}{4,250} \right) \times 100 = 0.2 \times 100 = 20\%
\]
Thus, **20%** of the total population of library card holders has been surveyed.