Dr. Johnson’s Pill Container Puzzle
Initial Scenario
Dr. Johnson possesses a container filled with pills. On the first day, he consumes half of the pills from this container.
Pill Consumption Over Days
On the second day, he takes half of the remaining pills. By the third day, he discovers that only 2 pills are left in the container.
Finding the Initial Number of Pills
To determine the initial quantity of pills, let x represent the original number of pills in the container.
On the first day, Dr. Johnson removes x/2 pills, leaving him with:
x – x/2 = x/2 pills.
On the second day, he takes half of the remaining pills:
1/2(x/2) = x/4 pills.
This leaves him with:
x/2 – x/4 = x/4 pills.
According to the situation, on the third day, only 2 pills remain in the container. Therefore, we set up the equation:
x/4 = 2.
Solving the Equation
To solve for x, we can multiply both sides of the equation by 4:
x = 8.
Thus, the initial number of pills in the container was 8.