Problem Statement
On the first day, a patient consumes one-third of the total pills from a container. The following day, the patient takes one-third of the remaining pills. In total, the patient has taken 15 pills from the container. The question arises: how many pills were initially present in the container?
Solution
Let X Represent the Initial Number of Pills
To find the initial number of pills, denote the total number of pills in the container as X.
Pills Taken on Each Day
On the first day, the patient takes one-third of the pills:
– First Day: (1/3)X pills are consumed.
On the second day, the patient takes one-third of the remaining pills:
– Remaining pills after the first day: X – (1/3)X = (2/3)X.
– Second Day: (1/3)(2/3)X = (2/9)X pills are consumed.
Establishing the Equation
The total number of pills taken over the two days can be expressed as:
(1/3)X + (2/9)X = 15.
Finding the Value of X
To solve for X, first, find a common denominator for the equation. The common denominator of 3 and 9 is 9. Rewriting the equation gives:
(3/9)X + (2/9)X = 15.
Combine the fractions:
(5/9)X = 15.
Now, multiply both sides by 9 to eliminate the fraction:
5X = 135.
Finally, divide by 5:
X = 27.
Conclusion
The initial number of pills in the container was 27.