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# Math help from the Learning Centre

This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

## Dosages Based on Body Weight

There are times where the size of the patient affects the amount of prescription prescribed. A child who weighs less will receive a smaller dose of the drug, or a patient with a larger body surface area will receive a larger dose. The size of the patient in relation to the dose can be expressed as the following

$Size\,of\,patient\times \,Order=\,Dose$

Examples:

1. A doctor orders phenytoin 15 mg/kg loading dose p.o., then 300 mg/d. You have the following drug available. a. how many mg of this anitconvulsant would you administer to a patient who weighs 80 kg?

body weight = 80 kg, order = 15 mg/kg, dose = ?

\begin{align} Size\,of\,patient\times \,Order&=\,Dose\\ 80\,kg\times\frac{15\,mg}{1\,kg}&=1200\,mg\end{align}

b. how many tablets would you administer?

$1200\,mg\times\frac{1\,tablet}{100\,mg}=12\,tablets$

2. An order of Vibramycin (doxycycline calcium) 2 mg/lb q.d. p.o. for 10 days. Use the label to determine how many millilitres of this antibiotic you would administer to a patient who weighs 90lb. Patient weight = 90 lb, order: 2 mg/lb, strength = 25 mg/5 mL

First, we need to calculate the dose based on the weight of the patient and the order.

$90\,lb\times\frac{2\,mg}{1\,lb}=180\,mg$

Every 5 mL of the solution contains 25 mg of the drug,

$180\,mg\times\frac{5\,mL}{25\,mg}=36\,mL$

The patient should receive 36 mL of Vibramycin every day for 10 days.

3. The physician orders Biaxin (clarithromycin) 7.5 mg/kg p.o. q.12.h.. If the drug strength is 250 mg/5 mL, how many mL of this antibiotic drug should be administered to a patient who weighs 154 pounds?

Since the weight of the patient is given in pounds, but the order is in kilograms, we have to convert the patients' weight into kilograms. Since $$1\,kg=2.2\,lb$$,

$154\,lb\times\frac{1\,kg}{2.2\,lb}=70\,kg$

Now, we find the dosage required of the order based on the size of the patient.

$70\,kg\times\frac{7.5\,mg}{kg}=525\,mg$

Finally, we convert into millilitres.

$525\,mg\times\frac{5\,mL}{250\,mg}=10.5\,mL$

The patient should receive 10.5 mL of Biaxin by mouth every 12 hours.

4. A 3-year-old child weighing 30 lb is prescribed to receive vancomycin hydrochloride (Vancocin) 30 mg/kg/day q.i.d. How many milligrams of the medication will the nurse provide the child for each dose?

Converting the child's weight to kg:

$30\,lb\times \frac{1\,kg}{2.2\,lb}=13.63636\,kg$

The order states 30 mg/kg/day. We can find the mg per day now that we have the child's weight in kg.

$\frac{30\,mg}{1\,kg}\times 13.63636\,kg=409.0909\,mg$

Each day, the child receives 409.0909 mg of Vancocin. Q.i.d. represents four times a day, the final step is to find the mg in each dose.

$\frac{409.0909\,mg}{1\,day}\times\frac{1\,day}{4\,dose}=102.2727\,mg$

The child will receive 102.3 mg (rounded to nearest tenth of a mg) of Vancocin each dose.