Challenging Brain Teaser for July 6: Sharpen Your Mind Today!

Patient Counts of Dr. Johnson and Dr. Smith

Overview

Dr. Johnson and Dr. Smith both had their own patients. An interesting scenario arises when the two doctors interact with each other’s patient lists.

Patient Exchange Scenarios

If Dr. Smith treated one of Dr. Johnson’s patients, they 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 both doctors, we can establish the following equations:
– Let x represent the number of patients Dr. Johnson saw.
– Let y represent the number of patients Dr. Smith saw.

The equations based on the scenarios are:
1. x – 1 = y + 1
2. x + 1 = 2 * (y – 1)

Solving these equations will provide the values for x and y.

Solution

From the first equation, we can deduce:
x – 1 = y + 1
=> x = y + 2

Substituting this into the second equation:
(y + 2) + 1 = 2 * (y – 1)
=> y + 3 = 2y – 2
=> 3 + 2 = 2y – y
=> y = 5

Now, substituting y back to find x:
x = 5 + 2
=> x = 7

To find the total number of patients seen by both doctors:
x + y = 7 + 5 = 12

Conclusion

In total, Dr. Johnson and Dr. Smith saw 12 patients together.