how many drops of medicine do you consume on average per hour of the days of treatment

[eddy2017]

HI, dear friends:
I need your help with this problem.
you have come down with an illness. You're expected to be fine as long as you take the exact amount of medicine that you need per day. However, your doctor only told you to take 5 mg of your medicine per kilogram of body weight, three times a day for two weeks. You weigh 170 lbs. and one drop of medicine contains 225 mg of your prescribed medicine. How many drops of your medicine do you consume on average per hour of the days of treatment. Assume 1 kg= 2.2 lbs..

Following a method that JeffM mentioned, (and which I am trying to apply and understand here). I am going to put in order all the information given to me.

Step I 'Getting all info out'.
5 mg of your medicine per kilogram of body weight.
3 times a day.
You weigh 170 pounds
One drop of medicine contains 225 mg of the prescribed medicine.
1 Kg = 2.2 pds
And what we are looking for is drops of the medicine on average per hour.

The method (Dimension Analysis) teaches me to identify value units and then conversion units or factors.

170 pds (value)
5 mg of your medicine per kilogram of body weight.( c.f)
3 times a day or 3 doses a day (c.f)
1 kg= 2.2 pounds (c.f)
1 drop of the medicine = 225 mg (c.f)

I want, if it is possible, and you consider that the right path to go, that you help me solve this following the dimension analysis theory.
I think it is a good method to work with this type of problems, only that I don't know what to do next.

Thank you very much for you much-needed and appreciated help.

 

[lev888]

I would start from the question and figure out what quantities I need.
How many drops on average per hour? Average per hour is the total number of drops per day divided by what?
Total number of drops per day is the amount of medicine per day divided by what?
Amount of medicine per day is 3 times 5 mg per kilogram of body weight. Which is 3 * 5 * what?
Do this until you define everything in terms of values and factors you are given. Then calculate everything.

 

[eddy2017]

Thanks for replying lev888. I will surely follow your lead. If I get stuck I will let you know.
thanksss!

 

[eddy2017]

Which is 3 * 5 * what?

3* 5 * 175 = 2625
Is this okay?
2.62 drops per day??
okay?

 

[lev888]

First, you need to finish defining everything. Then calculate. I haven't done it, so I can't say by looking at 175 without any explanation whether it's right or wrong.

 

[Dr.Peterson]

Take it step by step. There are lots of ways to proceed, which will lead to the same operations in different orders, so don't try to follow everyone's suggestion. Pick a way, show it to us, and we can talk about it.

I myself would suggest that you start (having already listed the data) with the goal: drops per hour. So start with drops: You know you need 1 drop per 225 mg of medicine. Now look for something related to milligrams of medicine: Ah! You take 5 mg per kilogram of body weight, 3 times a day. So to cancel out the mg, you can multiply by 5 mg/kg ...

But there's something tricky here. You aren't asked for anything about the total amount you take over the two weeks, or even each day, so some information may be unnecessary. How long is it, on average, between doses? That is what will really matter.

But, again, just make an attempt and talk through your thinking as I am doing, rather than just put down numbers or guess. Then we'll have something to help you fix.

 

[eddy2017]

my main issue is knowing when I have to multiply or divide to find something or to convert to something. I am sorry. I am stuck here even with Dr Peterson's explanation I can't make head or tails of this. I need the steps to how to use the reasoning behind what I am trying to do. I know there is a logical reasoning process broken down in steps, but if you do not show me, I will never get there. Thanks for trying to help.

 

[lev888]

Show your reasoning until the point where you are not sure whether to multiply or divide, we'll go from there.

 

[eddy2017]

okay, thanks, lev, I will give it my best shot. I will tell you what I am thinking and then you will correct me. it might not be in order, sort of in a hapzard way, but here I go.

5 mg of your medicine per kilogram of body weight.
if I know that the person weighs 170 lbs and then I know that 1 kg = 2.2
I will have to convert lbs to pounds 170 lb to kgs. Having the amount of kgs the person weighs will allow me to multiply them per 5 mg of the med.
is this okay?.
I do not know how to do it, though.
I read that to get kgs from pounds I divide by 2 and then take off 1/10 off of my answer, but did not understand how to do that.

 

[lev888]

One conversion method I like is setting up a proportion and solving it using the cross multiplication property. You don't need to worry what is a value and what is a conversion factor. Just list what you know and keep the same units on the same side:
1 kg is 2.2 lb
Unknown number of kg is 170 lb.

Use "x" for the unknown value and we have the following proportion:
1 kg --- 2.2 lb
x kg --- 170 lb

The cross multiplication property: put a big X through it, the products of values connected by the 2 lines are equal.
Therefore: 1kg * 170 lb = x kg * 2.2 lb
x = (1kg * 170lb)/2.2lb = ? kg

Video:

 

[eddy2017]

That was great!!!!. Thank you so much. I will continue tomorrow to finish the problem.

 

[JeffM]

In a previous post, Subhotosh Khan made the point that it may take some creativity and thought before you can even see how to apply the method of dimensional analysis.

It is frequently helpful in complex cases to come up with a new unit that lets you break the problem down into smaller pieces. In this problem, that unit is the "dose" of medicine prescribed. We see that

[MATH]\dfrac{x \text { doses}}{\text {hour}} * \dfrac{y \text { drops}}{\text {dose}} = \dfrac{x \cancel {\text { doses}}}{\text {hour}} * \dfrac{y \text { drops}}{\cancel { \text {dose}}}= \dfrac{xy \text { drops}}{\text {dose}}.[/MATH]
That makes obvious sense. And the doses per hour is easy.

[MATH]\dfrac{3 \text { doses}}{1 \text { day}} * \dfrac{1 \text { day}}{24 \text { hours}} = \dfrac{3 \text { doses}}{1 \cancel {\text { day}}} * \dfrac{1 \cancel {\text { day}}}{24 \text { hours}} = \dfrac{\dfrac{1}{8} \text { dose}}{\text {hour}}.[/MATH]
So y = 1/8.

The drops per dose is not so easy. The dose is not given in drops but rather as the ratio of milligrams of medicine relative to the patient's weight in kilograms and we have that weight in pounds. So there will be many steps of cancelling, but each is mechanical.

First, get rid of pounds.

[MATH]\dfrac{170 \text { lb. of body weight}}{1} * \dfrac{1 \text { kg. of body weight}}{2.4 \text { lb. of body weight}} = \dfrac{170 \cancel {\text { lb. of body weight}}}{1} * \dfrac{1 \text { kg. of body weight}}{2.4 \cancel {\text { lb. of body weight}}} =[/MATH]
[MATH]\dfrac{170}{2.4} \text {kg. of body weight}.[/MATH]
That makes sense; the weight in kilograms will be less than that in pounds. Next get rid of kg. of body weight.

[MATH] \dfrac{170}{2.4} \text { kg. of body weight} * \dfrac{5 \text { mg. of medicine}}{1 \text { kg. of body weight}} =[/MATH]
[MATH]\dfrac{170}{2.4} \cancel {\text { kg. of body weight}} * \dfrac{5 \text { mg. of medicine}}{1 \cancel {\text { kg. of body weight}}} = \dfrac{5 * 170}{2.4} \text { mg. of medicine} \implies[/MATH]
[MATH]\text {mg. of medicine per dose} = \dfrac{\dfrac{5 * 170}{2.4} \text { mg. of medicine}}{\text {dose}}.[/MATH]
That makes sense. The number of milligrams prescribed is 5 times the patient's body weight in kilograms. Now get rid of mg. of medicine.

[MATH]\dfrac{\dfrac{5 * 170}{2.4} \text { mg. of medicine}}{\text {dose}} * \dfrac{1 \text { drop}}{225 \text { mg. of medicine}} =[/MATH]
[MATH] \dfrac{\dfrac{5 * 170}{2.4} \cancel {\text { mg. of medicine}}}{\text {dose}} * \dfrac{1 \text { drop}}{225 \cancel {\text { mg. of medicine}}} = \dfrac{\dfrac{5 * 170}{2.4 * 225} \text { drops}}{\text {dose}}.[/MATH]
Again, multiplying milligrams per dose times drops per milligram is a sensible way to get rid of milligrams and finally gets us to drops per dose.

So x = (5 * 170)/(2.4 * 225).

[MATH]xy = \dfrac{5 * 170}{2.4 * 225 * 8} \approx 0.2 \text { drops per hour}.[/MATH]

 

[eddy2017]

Complex but great.
A couple of questions.
Where does 2.4 come from?
Where does the 8 at the end come from?
Thanks.

 

[JeffM]

Oh. That should have been 2.2. Duh! Sorry. My proofing on that one was totally dominated by LaTex.

The 8 comes from 3 doses per day, or 3 does per 24 hours, or 1 dose per 8 hours. Look at line 2 of the LaTeX.

 

[eddy2017]

Okay, good. Thanks a million, Jeff. Now, I will have to study all this. I copy down everything you all say.