proton pump inhibitors

Dr. Johnson has a container with pills.
On the first day he takes half of the pills from the container.
On the second day he takes half of the pills that remained in the container.
On the third day he noticed that only 2 pills remained in the container.
How many pills were there in the container to begin with?

See the answer

Answer: 8

Let x be the initial number of pills in the container.
Then on the first day Dr. Johnson took x/2 pills, so there were x-x/2 pills left in the container.
Hence, on the second day he took ½(x-x/2) pills.
Therefore, x-1/2(x-x/2) = 2 or x- 1/2x – 1/4x=2.
Multiplying both parts by 4, we get 4x – 2x – x =8, so x=8.

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