Question #410ad

1 Answer
Sep 25, 2017

Answer:

Here's what I got.

Explanation:

You can start by calculating the total number of grams of this drug that the patient needs in #1# day.

Since you know that the dosage is set at #"1.9 g"# every #"6 h"#, you can say that the patient will need

#"1.9 g/6 h" = "1.9 g"/(6color(red)(cancel(color(black)("hours")))) * (24color(red)(cancel(color(black)("hours"))))/"1 day" = "7.6 g"/"1 day" = "7.6 g/day"#

Next, use the fact that

#color(blue)(ul(color(black)("1 g" = 10^3color(white)(.)"mg")))#

to convert the sample to milligrams

#7.6 color(red)(cancel(color(black)("g"))) * (10^3color(white)(.)"mg")/(1color(red)(cancel(color(black)("g")))) = 7.6 * 10^3color(white)(.)"mg"#

So, you know that your patient needs #7.6 * 10^3# #"mg"# of this drug per day. To find the number of tablets needed to deliver this sample to the patient, use the fact that #1# tablet has a mass of #"500 mg"#.

#7.6 * 10^3 color(red)(cancel(color(black)("mg"))) * "1 tablet"/(500color(red)(cancel(color(black)("g")))) = "15.2 tablets"#

Now, if you cannot split a table into #5# equal parts so that you can give

#15.2 = 15 1/5#

tablets to the patient--which would be consistent with the fact that the answer must have #1# significant figure--then my guess is that #"1.9 g"# is a typo and that the actual value is #"1.0 g"#.

In this case, you have

#"1.0 g/6 h = 4 g/day"#

which means that you will need

#4 * 10^3 color(red)(cancel(color(black)("mg"))) * "1 tablet"/(500color(red)(cancel(color(black)("mg")))) = "8 tablets"#

Since the values given to you justify a #1#-sig-fig answer, this is most likely what the problem looked like.