Question

one particular drug is in many non - prescription medications, making it easy to get more than the 400 milligrams per day linked to health problems and the recommended 325 - milligram daily maximum. a painkiller contains 500 milligrams of the drug per pill. a cold medicine contains 325 milligrams of the drug per pill.
a. what is the maximum number of painkiller pills that should be taken in 24 hours?
b. if you take one painkiller pill per hour for two hours, what is the maximum number of cold medicine pills that should be taken for the remainder of 24 hours?
(type a whole number.)
(type a whole number.)

Explanation:

Step1: Calculate number of 2 - hour intervals in 24 hours

$24\div2 = 12$

Step2: Find maximum number of pain - killer pills

Since 1 pain - killer pill can be taken per 2 - hour interval, the maximum number of pain - killer pills is 12.

Step3: Calculate remaining drug amount after pain - killer intake

The maximum daily drug intake is 3250 milligrams. Each pain - killer pill has 500 milligrams. So the drug from pain - killer pills is $12\times500=6000$ milligrams which is already over the limit. But if we assume we take the maximum amount allowed by the limit for pain - killers, the number of pain - killer pills we can take is $\lfloor\frac{3250}{500}
floor = 6$ (using the floor function as we can't take a fraction of a pill).

Step4: Calculate remaining drug amount for cold medicine

The drug from 6 pain - killer pills is $6\times500 = 3000$ milligrams. The remaining amount for cold medicine is $3250−3000=250$ milligrams. Each cold medicine pill has 325 milligrams, so the number of cold medicine pills is $\lfloor\frac{250}{325}
floor = 0$

Answer:

a. 6
b. 0