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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.

## Intravenous (IV) Piggyback Solutions

Patients can receive a second infusion using an IV piggyback line hung alongside the first. Usually, a secondary IV interrupts the administration of the primary IV medication. The primary IV resumes after the secondary IV has finished. Since the two lines do not mix, we only need to calculate the flow and dosage rates for the secondary line.

## Examples

1. An IVPB is infusing at $$120\, mL/h$$. The concentration is 50 mg in 100 mL of NS. What is the dosage rate in mg/min?

There are a few things we need to convert to get $$120\, mL/h$$ to the dosage rate of mg/min. First, we can infuse the concentration of 50 mg in 100 mL of NS.

$\frac{120\, mL}{1\, h}\times\frac{50\, mg}{100\, mL}=\frac{60\,mg}{1\, h}$

Next, we need to convert hours into minutes

$\frac{60\, mg}{1\, h}\times\frac{1\, h}{60\,min}=1\,mg/min$

The dosage rate for this IV piggyback is 1 mg/min.

2. Your patient is a 125 lb adult. An order for Tagamet 5mg/kg in 50 ml D5W IVPB to be infused in 20 minutes. Use the label below with the drop factor 10 gtts/mL.

a. How many mL of Tagamet will you add to the IV fluid?

First, we have to find the weight of the patient in kg.

$125\,lb=\frac{1\,kg}{2.2\,lb}=56.82kg$

The order for Tagamet is for 5 mg/kg.

$56.82\,kg\times\frac{5\,mg}{1\,kg}=284.1\,mg$

Thus the order should be 284.1 mg.

Next, the Tagament strength from the label is 300mg/2mL.

$284.1\,mg\times\frac{2\,mL}{300\,mg}=1.9\,mL$

1.9 mL should be added to the IV.

b. What will be your flow rate in gtts/min?

First, we convert Tagamet in 50 mL using the drop factor 10 gtt/mL.

$50\,mL\times\frac{10\,gtt}{1\,mL}=500\,gtt$

Then we find the flow rate by dividing the time of 20 minutes.

$\frac{500\,gtt}{20\,min}=25\,gtt/min$

c. In mL/h?

Converting 50 mL in 20 minutes to mL/h

$\frac{50\,mL}{20\,min}\times\frac{60\,min}{1\,h}=150\,mL/h$

3. An order of morphine sulfate 200 mg IVPB in NS 1000 mL to be infused at a rate of 20 mcg/kg/h stat. The patient weighs 134 kg.

a. How many mg/h of this narcotic analgesic will the patient receive?

First, we calculate the mcg required for a patient weighing 134 kg at the infusion rate of 20 mcg/kg.

$134\,kg\times\frac{20\,mcg}{1\,kg}=268\,mcg$

Now we convert the 268 mcg/h to mg/h

$\frac{268\,mcg}{1\,h}\times\frac{1\,mg}{1000\,mcg}=2.68\,mg/h$

The patient will receive 2.68 mg/h IVPB immediately.

b. How many mL/h of the solution will the patient receive?

The order of 200 mg IVPB in NS 1000 mL can be used with the 2.68 mg/h to calculate the mL/h to be administered.

$\frac{1000\,mL}{200\,mg}\times\frac{2.68\,mg}{1\,h}=13.4\,mL/h$

The patient will receive 13.4 mL/h of morphine sulfate.