Question

A patient needs to take 875 mg of ibuprofen twice daily. The pills in the bottle are each 250. mg. How many pills does the patient need to take each time she wants the 875 mg dosage? Assume that these pills are scored and can be cut in half if necessary.

Answer 1

If the patient needs to take 875 mg every day 'twice a day' then the patient needs to take 3 whole pills and one half pill to make up the 875 mg, then the patient will have to do that twice cause it says "twice daily". 

Let me show below: 1 pill = 250   mg
                                 1 pill = 250   mg 
                                 1 pill = 250   mg 
                          half a pill = 125   mg   Add them together
                                         ----------    
                                             875 mg      (don't forget the patient has to take 875 twice daily so in a full day the patient will have to take 7 whole pills)

Hope this helps! If u need anything else just ask! :)
                      

Answer 2

The patient needs to take 3 and 1/2 pills to get the required 875 mg dosage. The patient, therefore, will have to take a total of 7 pills daily.

Further Explanation

This problem can be quickly solved using dimensional analysis. Dimensional analysis is a method of solving problems using the known units of measurements of the quantities given in a problem. The steps include:

1. Sort the given in the problem.
2. Set up the dimensional analysis to get the desired value.

STEP 1: Sorting the given in the problem gives the required conversion factors:

1 pill = 250. mg of ibuprofen

1 dose = 875 mg of ibuprofen

STEP 2: Setting up the dimensional analysis to get the equivalent number of pills of 875 mg:

$no. \ of \ pills = 875 \ mg \times \frac{1 \ pill}{250. \ mg}\\\boxed {no. \ of \ pills \ = 3.50 \ pills}$

The patient will need to take 3 and a half pills twice a day to get the daily recommended dosage (875 mg) of ibuprofen.

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Keywords: word problem, dimensional analysis, ibuprofen, dosage, conversion factor