Unit Conversion/ratio

daigo

A medicinal dosage is 5 milligrams per pound of bodyweight. The medicine is 0.9 grams per milliliter. If a patient is 72.7 kilograms, how many milliliters of dosage should the patient take?
Okay I did the easy part first:

5 mg / 1 lb = .005 g / 1 lb

Since there's .005 grams in 5 milligrams. Now I will change it to kilograms:

.005 g / 1 lb = x / 2.20462262 lb

Since there's 2.20462262 lbs. in 1 kg so I want the ratio set for grams per kilogram (since 1 kg is 2.20462262 lbs. and I need to keep the units in lbs)

Cross multiply:

.005 g / 1 lb = x / 2.20462262 lb

(2.20462262 lb)(.005 g) = (1 lb)(x)

Divide both sides by 1 lb which cancels out the lb. unit on both sides:

(2.20462262)(.005 g) = x

So:

0.0110231131 g = x

So I will need 0.0110231131 grams per 2.20462262 lbs. of body weight. 2.20462262 lbs is also 1 kg so I will just exchange the units:

0.0110231131 grams / 1 kg

The dosage is 0.0110231131 grams per 1 kg, so:

0.0110231131 grams / 1 kg = x / 72.7 kilograms

Cross multiply:

(1 kg)(x) = (0.0110231131 grams)(72.7 kilograms)

Divide both sides by 1 kg:

x = (0.0110231131 grams)(72.7)

x = 0.801380322 grams

So the patient needs 0.801380322 grams of medicine total for his bodyweight.

What I don't understand is what to do next. What does 0.9 grams per milliliter mean? I thought milliliter is a unit of volume. So that means there's 0.9 grams of medicine per 1 milliliter of volume (of maybe water or some other physical space, maybe like in pill form or otherwise), but what does that have to do with problem or anything at all?

I know I get the correct answer if I divide: 0.801380322 grams / (.9 grams / 1 mL)

But I don't understand the reason why.

greg1313

Forum Staff
diago said:
What does 0.9 grams per milliliter mean?
This means there are 900 milligrams (0.9 grams) of medicine in 1 milliliter of solution (I'm assuming it is a liquid, but as you pointed out it may be a solid (e.g. a pill)).

diago said:
I thought milliliter is a unit of volume.
That is correct. It is a measure of volume.

I know I get the correct answer if I divide: 0.801380322 grams / (.9 grams / 1 mL)
The dosage should be about 0.8904 milliliters. You take the weight in pounds and multiply that by 5: 160.276065 * 5 = 801.380325. So the patient needs 801.380325 milligrams of medicine. Since there are 900 milligrams of medicine per milliliter, the patient needs 801.380325/900 milliliters or about 0.8904 milliliters.

Here's another example: Say we have a solution that contains 50 mg. of medicine per milliliter and we want to administer 10 mg of medicine. We need 1/5 of 50 = 10 mg so we administer 10/50 = 0.2 ml of solution.

agentredlum

Math Team
In a solution of 1 ml there is 0.9 g of medicine. You need to give the patient 0.801g of medicine in liquid form so do

1ml/(0.9g) = x/(0.801g)