Let's call the total number of people surveyed $x$.
Out of those surveyed, 86.8% believed that rats carry diseases. This means that 86.8% of $x$ people believed that rats carry diseases, or $0.868x$ people.
Out of those who believed that rats carry diseases, 45.7% mistakenly believed that rats frequently carry rabies. This means that 45.7% of $0.868x$ people mistakenly believed that rats frequently carry rabies, or $0.457(0.868x) = 0.396076x$ people.
We know that 21 people were incorrect in their belief about rats carrying rabies.
Therefore, we can set up the equation $0.396076x = 21$ and solve for $x$.
Dividing both sides of the equation by $0.396076$, we get $x = \frac{21}{0.396076} \approx \boxed{53}$.
The answer is: 53
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
John conducted a survey on people's knowledge of rats. Rounded to the nearest tenth of a percent, 86.8% of the surveyed individuals believed that rats carry diseases. Out of those who thought rats carried diseases, 45.7% mistakenly believed that rats frequently carry rabies. Since rats do not frequently carry rabies, these 21 people were incorrect. How many people in total did John survey?

### Answer:
