Pill Consumption Problem

Initial Scenario

Dr. Johnson possesses a container filled with pills. On the first day, he consumes half of the pills present in the container.

Pill Consumption Over Days

On the second day, Dr. Johnson takes half of the remaining pills. By the third day, he discovers that only 2 pills are left in the container.

Calculating the Initial Number of Pills

To determine the initial quantity of pills in the container, let x represent this number.

Day-by-Day Breakdown

On the first day, Dr. Johnson takes x/2 pills, leaving him with:
x – x/2 = x/2 pills in the container.

On the second day, he consumes half of the remaining pills:
1/2(x – x/2) = 1/2(x/2) = x/4.

After the second day, the number of pills left is:
x/2 – x/4 = (2x/4 – x/4) = x/4.

Setting Up the Equation

According to the problem, after the second day, only 2 pills remain, leading to the equation:
x/4 = 2.

Solving the Equation

Multiplying both sides by 4 gives:
x = 8.

Conclusion

Thus, the initial number of pills in the container was 8.