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This is super basic, but I have not been in school for YEARS. I am a bit dusty. Any-who, Its a common word problem, and as follows: A licensed practical nurse gives 1800 milligrams of penicillin over a 36 hour time period. If the dosage occurs every 6 hours, how many milligrams are in each dose if the dose is the same amount each time?

Robert
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2 Answers2

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Problems like these are prone to the so-called "off-by-one" or "fencepost error", which you can read about, e.g., here: https://en.wikipedia.org/wiki/Off-by-one_error

To avoid it, you have to be very clear what you mean.

My reading of this question would be this: let's pick a start time: Midnight Sunday morning, say, for the first dose. Last dose is $36$ hours later, at noon on Monday. The full list of doses given is:

$$\{12\; AM, 6\; AM, 12\; PM, 6\; PM, 12\;AM, 6\;AM, 12\;PM\}$$

Hence, $7$ doses all in all. Assuming this is what is intended, the answer would then be $$\frac {1800}{7}\;\sim\;257.143$$

lulu
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  • If you were taking a course of antibiotics over a length of 2 weeks you'd receive only 14 tablets. You wouldn't receive tablets for the 15th day. – RowanS Sep 02 '15 at 00:30
  • @RowanS I would understand "a length of 2 weeks" to mean "one a day, each day, for two weeks". Hence 14. No ambiguity. I suppose you could read it as "every 24 hours starting with midnight on Jan 1 and ending at midnight on Jan 15" in which case you'd want that $15^{th}$ pill. But I don't think I'd read it that way. Similarly, if the OP had said "doses were given once an hour for 36 hours" I think we'd all interpret that as 36 doses. But, the ambiguity comes from casual use of language. To avoid, it I'd ask when, exactly, doses were to be given. – lulu Sep 02 '15 at 00:35
  • @RowanS And, if the course started with the first pill at noon on Monday. you'd have no pill to take at noon, Monday, two weeks later. So the last pill was taken 13 days after the first... – DJohnM Sep 02 '15 at 00:37
  • Pharmacists are aware of this problem, naturally: I just finished two such courses of medication (pain and antibiotics, don't ask) and the vials both say "Take 1 tablet, 3 times a day, until exhausted" – DJohnM Sep 02 '15 at 00:39
  • @DJohnM And, judging from the prescriptions, I expect you were exhausted before the first dose. Speaking of ambiguous wording, I mean. – lulu Sep 02 '15 at 00:40
  • this problem comes up constantly in Finance as well. You have cash flows every 6 months for X years. How many payments are we speaking of? The ambiguity is resolved by writing out exactly the days on which payments will be made. Only way to be sure. – lulu Sep 02 '15 at 00:43
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So we divide 36 by 6 to get the number of doses the nurse gives which is 6. We then divide the mass of penicillin by the number of doses the nurse gave. So 1800/6=300 milligrams.

So therefore there are 300 milligrams of penicillin in each dose.

RowanS
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