Problem Overview
In a mental health hospital, there is one doctor and numerous patients. Each day, every patient engages in a behavior where they bite someone, which may also lead to self-inflicted injuries.
Daily Biting Behavior
Over the course of seven days, each patient bites twice. Meanwhile, the doctor experiences a total of 100 bites during this period.
Mathematical Representation
Let x represent the number of patients in the clinic. The total number of bites over seven days can be formulated as follows:
- Total bites from patients: 7x
- Total bites experienced by the doctor: 2x + 100
Solving the Equation
By setting the total bites equal to each other, we have the equation:
7x = 2x + 100
Solving for x gives us:
Conclusion
After simplifying the equation, we find that x = 20. Therefore, there are 20 patients in the clinic.