Solveeit Logo
Login

Question

Question: The doctor orders a medication as \( 5.00{\text{ mg k}}{{\text{g}}^{ - 1}} \) of body weight. The do...

The doctor orders a medication as 5.00 mg kg−15.00{\text{ mg k}}{{\text{g}}^{ - 1}} of body weight. The dosage the nurse gives the patient is 425 mg{\text{425 mg}} . How much does the patient weigh in pounds?

Explanation

Solution

The doctor gives the medication according to the weight of the patient which is measured in kilograms. Now we have to convert this kilogram into pounds which is another unit of measuring weight. We will use the conversion factor of converting weight in kilograms into weight in pounds. Then we will find the weight of the patient who needs 425 mg{\text{425 mg}} of the given dose.

Complete Step By Step Answer:
When we go to the doctor then the doctor prescribes us a medicine which has some specifications according to our weight. According to the question, the medicine which was ordered by the doctor for medication has specifications as 5.00 mg kg−15.00{\text{ mg k}}{{\text{g}}^{ - 1}} of body weight. Now we are asked the weight of the patient in pounds therefore we have to convert the units of prescribed dose in terms of pounds. We will use the conversion factor as:
1 kg ≅ 2.2046 lbs1{\text{ kg }} \cong {\text{ 2}}{\text{.2046 lbs}} ,where lbs is the unit of pounds.
Thus 5.00 mg kg−15.00{\text{ mg k}}{{\text{g}}^{ - 1}} can be written as:
⇒ 5.00 mgkg\Rightarrow {\text{ }}5.00{\text{ }}\dfrac{{{\text{mg}}}}{{kg}}
Using the above conversion factor we can write as:
⇒ 5.00 mg2.2046 lbs\Rightarrow {\text{ }}5.00{\text{ }}\dfrac{{{\text{mg}}}}{{2.2046{\text{ lbs}}}}
⇒ 5.002.2046 mg lbs\Rightarrow {\text{ }}\dfrac{{5.00}}{{2.2046}}{\text{ }}\dfrac{{{\text{mg}}}}{{{\text{ lbs}}}}
⇒ 2.268 mg lbs\Rightarrow {\text{ 2}}{\text{.268 }}\dfrac{{{\text{mg}}}}{{{\text{ lbs}}}}
Thus in terms of pounds the prescribed dose can be written as 2.268 mg lbs−1{\text{2}}{\text{.268 mg lb}}{{\text{s}}^{ - 1}} . Now according to the question the nurse gave 425 mg{\text{425 mg}} of this dose to the patient. Thus the total weight of the patient can be found as:
⇒ 425 mg2.268 mg lbs−1\Rightarrow {\text{ }}\dfrac{{{\text{425 mg}}}}{{{\text{2}}{\text{.268 mg lb}}{{\text{s}}^{ - 1}}}}
On solving the above equation we get the result as:
⇒ 187.39 lbs\Rightarrow {\text{ 187}}{\text{.39 lbs}}
Thus the weight of the patient in pounds will be equal to 187.39 lbs{\text{187}}{\text{.39 lbs}} .

Note:
We can take the approximate value of pounds in one kilogram. The weight of the patient can be taken as 187 lbs{\text{187 lbs}} which is also correct as it is a round-off value of 187.39 lbs{\text{187}}{\text{.39 lbs}} . If we are asked to find the weight of a patient in kilograms then there is no need to convert the weight into pounds , else the rest of the steps will be the same.