Challenging Brain Teaser for August 12: Boost Your Mental Skills Today

Patient Interaction Analysis

Overview

Dr. Johnson and Dr. Smith both attended to patients. Their interactions with each other’s patients led to specific numerical relationships regarding the number of patients they saw.

Patient Relationships

If Dr. Smith attended to one of Dr. Johnson’s patients, then both doctors would have seen an equal number of patients. Conversely, if Dr. Johnson treated one of Dr. Smith’s patients, he would have seen twice as many patients as Dr. Smith.

Calculating Total Patients

To determine the total number of patients seen by Dr. Johnson and Dr. Smith together, we can establish equations based on the information provided.

Let:
– x = number of patients Dr. Johnson saw
– y = number of patients Dr. Smith saw

From the given conditions, we can formulate the following equations:
1. x – 1 = y + 1
2. x + 1 = 2 * (y – 1)

By solving these equations, we find:
– From the first equation: x – y = 3 (1)
– From the second equation: x – 2y = -3 (2)

Solving these equations yields:
– From equation (1): x = y + 3
– Substituting into equation (2): (y + 3) – 2y = -3
– This simplifies to y = 6.

Substituting y back into equation (1):
– x = 6 + 3 = 9.

Thus, we have:
– x = 7
– y = 5

Final Calculation

The total number of patients seen by both doctors is:
x + y = 7 + 5 = 12.

Therefore, the combined total of patients seen by Dr. Johnson and Dr. Smith is 12.