Understanding the Problem
To find out how many people were surveyed based on the given percentage of folk music enthusiasts, we can use the information provided. We know that 30% of the surveyed people liked folk music, and that number is equivalent to 20 people.
Setting Up the Equation
Let’s denote the total number of people surveyed as \( x \). According to the problem:
- 30% of \( x \) equals 20 people.
This can be represented mathematically as:
\[ 0.30 \times x = 20 \]
Solving for \( x \)
To find \( x \), we need to isolate it in the equation:
- Divide both sides by 0.30:
\[ x = \frac{20}{0.30} \]
- Calculate the value:
\[ x = \frac{20}{0.30} = \frac{20 \times 100}{30} = \frac{2000}{30} \]
- Simplifying the fraction, we get:
\[ x = \frac{2000 \div 10}{30 \div 10} = \frac{200}{3} \approx 66.67 \]
Since we cannot have a fraction of a person, we round to the nearest whole number, which is 67.
Final Answer
Thus, the total number of people surveyed is approximately:
- 67 people
This means that if 30% of the surveyed population liked folk music, then a total of 67 people were surveyed, resulting in 20 people expressing their preference for folk music.