Question

The doctor orders a medication as `"5.00 mg/kg"` of body weight. The dosage the nurse gives the patient is `"425 mg"`. How much does the patient weigh in pounds?

Answer 1

`"187 lbs"`

Explanation:

You have a little mor econverting to do to solve this one.

You know that the drug dosage is set to `"5.00 mg/kg"` of body weight, and that you need to give the patient's weight in pounds.

To start, you can convert the dosage from miligrams per kilogram to miligrams per pound by using the conversion factor

`"1 kg" ~= "2.2046 lbs"`

This means that you have

`5.00"mg"/color(red)(cancel(color(black)("kg"))) * (1color(red)(cancel(color(black)("kg"))))/"2.2046 lbs" = "2.268 mg/lbs"`

So, your patient needs 2.268 mg of the drug per pound of body weight. This means that if you supply 425 mg, his body weight must be

`425color(red)(cancel(color(black)("mg"))) * "1 lbs"/(2.268color(red)(cancel(color(black)("mg")))) = "187.39 lbs"`

Rounded to three sig figs, the number of sig figs you gave for the dosage and mass of drug administered, the answer will be

`color(green)("187 lbs")`

Answer 2

The patient weighs `"187 lb"`.

Explanation:

Given/Known

Medication mass/body mass: `"5.00mg/kg"`

Dosage: `"425 mg"`

`"1 kg"` `=` `"2.2 lb"`

`425cancel "mg"xx(1"kg")/(5.00cancel "mg")="85 kg"`

`85 cancel"kg"xx(2.2 "lb")/(1 cancel"kg") ="187 lb"`

Answer 3

Just over 187 lb

Explanation:

`M = D times W` where M is the medication mass in mg, D is the dose rate in mg per kg, and W is the weight of the patient in kg.

Therefore `W = M/D`

But you want the weight of the patient in lb, so you need to build in the conversion `lb = kg times 2.205`.

Therefore the final equation is: `W = (M/D) times 2.205`

Plug in the numbers and you get 187.43 lb.