Medical math practice problems for calculating IV pump settings and medication dosages.

Let's solve each of these medication calculation problems step by step.

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1. Nitroglycerin: 25 mg in 250 mL D5W, administer 7 mcg/min

Goal: Find mL/hr to set on IV pump.

#### Step 1: Convert concentration to mcg/mL
- 25 mg = 25,000 mcg (since 1 mg = 1,000 mcg)
- Total volume = 250 mL

So, concentration:
\[
\frac{25,000 \text{ mcg}}{250 \text{ mL}} = 100 \text{ mcg/mL}
\]

#### Step 2: Determine how many mL per minute for 7 mcg/min
\[
\frac{7 \text{ mcg/min}}{100 \text{ mcg/mL}} = 0.07 \text{ mL/min}
\]

#### Step 3: Convert to mL/hr
\[
0.07 \text{ mL/min} \times 60 \text{ min/hr} = 4.2 \text{ mL/hr}
\]

✔ Answer: 4.2 mL/hr

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2. Heparin: 25,000 units in 250 mL D5W, administer 8,000 units/hr

Goal: mL/hr

#### Step 1: Concentration
\[
\frac{25,000 \text{ units}}{250 \text{ mL}} = 100 \text{ units/mL}
\]

#### Step 2: mL/hr needed for 8,000 units/hr
\[
\frac{8,000 \text{ units/hr}}{100 \text{ units/mL}} = 80 \text{ mL/hr}
\]

✔ Answer: 80 mL/hr

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3. Dopamine: 12 mcg/kg/min, patient weighs 187 lbs, dopamine 800 mg in 250 mL D5W

Goal: mL/hr

#### Step 1: Convert weight to kg
\[
187 \text{ lbs} \div 2.2 = 85 \text{ kg}
\]

#### Step 2: Calculate total dose required per minute
\[
12 \text{ mcg/kg/min} \times 85 \text{ kg} = 1,020 \text{ mcg/min}
\]

#### Step 3: Convert to mcg/hr
\[
1,020 \text{ mcg/min} \times 60 = 61,200 \text{ mcg/hr}
\]

#### Step 4: Convert dopamine concentration
- 800 mg = 800,000 mcg
- Volume = 250 mL

Concentration:
\[
\frac{800,000 \text{ mcg}}{250 \text{ mL}} = 3,200 \text{ mcg/mL}
\]

#### Step 5: mL/hr
\[
\frac{61,200 \text{ mcg/hr}}{3,200 \text{ mcg/mL}} = 19.125 \text{ mL/hr}
\]

✔ Answer: 19.1 mL/hr (rounded to nearest tenth)

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4. Tagamet IVPB: 300 mg in 50 mL over 30 minutes, drop factor = 60 gtt/mL

Goal: gtt/min

#### Step 1: mL/min
\[
\frac{50 \text{ mL}}{30 \text{ min}} = 1.666... \text{ mL/min}
\]

#### Step 2: Convert to drops per minute
\[
1.666 \text{ mL/min} \times 60 \text{ gtt/mL} = 100 \text{ gtt/min}
\]

✔ Answer: 100 gtt/min

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5. Unasyn IVPB: 1 g in 100 mL over 30 minutes

Goal: mL/hr

#### Step 1: Time in hours
\[
30 \text{ min} = 0.5 \text{ hr}
\]

#### Step 2: mL/hr
\[
\frac{100 \text{ mL}}{0.5 \text{ hr}} = 200 \text{ mL/hr}
\]

✔ Answer: 200 mL/hr

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6. Lanoxin: Order is 0.25 mg po, on hand is 0.5 mg/2 mL

Goal: How many mL?

#### Step 1: Use ratio-proportion
\[
\frac{0.5 \text{ mg}}{2 \text{ mL}} = \frac{0.25 \text{ mg}}{x \text{ mL}}
\]

Cross-multiply:
\[
0.5x = 0.5 \Rightarrow x = 1 \text{ mL}
\]

✔ Answer: 1 mL

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✔ Final Answers:

1. 4.2 mL/hr
2. 80 mL/hr
3. 19.1 mL/hr
4. 100 gtt/min
5. 200 mL/hr
6. 1 mL

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