NCLEX: Drug Dosage Calculation Exam 9

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Wilson must administer 15 mg of morphine intramuscularly. The available morphine injection is labeled as grain 1/6 per mL. To determine the required volume in mL, we first convert the concentration from grains to mg and then calculate the volume needed.

Step-by-Step Calculation:

1. Convert the concentration from grains to milligrams:

• Conversion factor: 1 grain = 64.8 mg
• Thus, 1/6 grain = 64.8 mg ÷ 6 = 10.8 mg/mL

2. Calculate the required volume:

• Ordered dose = 15 mg
• Volume required = 15 mg × (1 mL / 10.8 mg)
• The mg units cancel, leaving: 15 ÷ 10.8 ≈ 1.39 mL

3. Rounding:

• Rounded to the nearest option, approximately 1.5 mL

Final Answer:

• Nurse Wilson should prepare 1.5 mL of the morphine injection.

ANSWER: 1.5 mL

Simplified recap: Convert 1/6 grain to mg (1/6 grain = 10.8 mg) and then divide the ordered dose (15 mg) by 10.8 mg/mL to get about 1.39 mL, which rounds to 1.5 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Garcia must administer diazepam 8 mg IV push stat. The available diazepam injection has a concentration of 5 mg per mL. We need to calculate the volume in milliliters that will deliver 8 mg of diazepam.

Step-by-Step Calculation:

1. Identify the given values:

• Ordered dose: 8 mg
• Concentration: 5 mg per 1 mL

2. Set up the conversion using dimensional analysis:

Volume required = 8 mg × (1 mL / 5 mg)

• The unit mg cancels out, leaving the result in mL.

3. Perform the calculation:

• 8 ÷ 5 = 1.6 mL

Final Answer:

• Nurse Garcia should draw up 1.6 mL of the diazepam injection.

ANSWER: 1.6 mL

Simplified recap: Divide the ordered dose (8 mg) by the concentration (5 mg/mL) to obtain 1.6 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Alana is monitoring an aminophylline infusion running at 20 mL/hour. The IV solution is 100 mg per 100 mL, so its concentration is 1 mg per mL. The patient weighs 130 pounds, and the safe maintenance dose is 0.36 mg/kg/hour. We need to verify the actual dose in mg/hour and compare it to the safe range.

Step-by-Step Calculation:

1. Determine the dose administered per hour:

• Concentration = 100 mg/100 mL = 1 mg/mL
• Infusion rate = 20 mL/hour
• Dose per hour = 20 mL/hour × 1 mg/mL = 20 mg/hour

2. Convert the patient’s weight from pounds to kilograms:

• 1 lb ≈ 0.4536 kg
• Weight in kg = 130 lb × 0.4536 kg/lb ≈ 59 kg

3. Calculate the safe dose based on weight:

• Safe dose = 0.36 mg/kg/hour
• Safe dose in mg/hour = 0.36 mg/kg/hour × 59 kg ≈ 21.24 mg/hour

4. Compare the administered dose with the safe dose:

• Administered dose = 20 mg/hour
• Safe dose ≈ 21.24 mg/hour
• Since 20 mg/hour is below 21.24 mg/hour, the infusion is within the safe range.

Final Answer:

• Patient is receiving 20 mg/hour; yes, the dose is safe.

Simplified recap: With a concentration of 1 mg/mL, 20 mL/hour delivers 20 mg/hour. For a 59 kg patient, a safe dose is approximately 21.24 mg/hour (0.36 mg/kg/hour × 59 kg), so 20 mg/hour is safe.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Rodriguez must administer 10 mg of prochlorperazine via intramuscular injection. The available injection is labeled as 5 mg per mL. The task is to determine the volume (in mL) that will deliver the correct dose.

Step-by-Step Solution:

1. Identify the given values:

• Ordered dose: 10 mg
• Concentration: 5 mg per 1 mL

2. Set up the conversion using dimensional analysis:

10 mg × (1 mL / 5 mg)

• The unit mg cancels out, leaving the result in mL.

3. Perform the calculation:

• 10 ÷ 5 = 2 mL

Final Answer:

• Nurse Rodriguez should draw up 2 mL of the prochlorperazine injection.

ANSWER: 2 mL

Simplified recap: Divide the ordered dose (10 mg) by the concentration (5 mg per mL) to obtain 2 mL, with the mg units cancelling out.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Rodriguez must infuse 50 mL of ceftriaxone in D5W over 20 minutes using IV tubing with a drip factor of 10 drops per mL. The goal is to determine the drip rate in drops per minute.

Step-by-Step Calculation:

1. Calculate the infusion rate in mL per minute:

• Total volume = 50 mL
• Total time = 20 minutes
• Infusion rate = 50 mL ÷ 20 min = 2.5 mL/min

2. Convert the rate to drops per minute using the drop factor:

• Drip rate = 2.5 mL/min × 10 drops/mL = 25 drops per minute

Final Answer:

• Nurse Rodriguez should set the drip rate to 25 drops per minute.

ANSWER: 25 drops per minute

Simplified recap: Dividing 50 mL by 20 minutes gives 2.5 mL/min, and multiplying 2.5 mL/min by the drop factor of 10 yields 25 drops per minute.

EXPLANATION

✔Solution:

Understanding the Problem:

Mr. Clark must restrict his daily fluid intake to 2 liters, and Nurse Evans needs to explain this in terms of standard household cups. We need to convert 2 liters (2000 mL) into cups, using the standard conversion factor (1 cup = 240 mL).

Step-by-Step Calculation:

1. Convert liters to milliliters:

• 2 liters = 2000 mL

2. Use the conversion factor for cups:

• 1 cup = 240 mL

3. Calculate the number of cups:

• Number of cups = 2000 mL ÷ 240 mL/cup ≈ 8.33 cups

4. Interpret the Result:

• This is equivalent to approximately 8 and 1/3 cups per day.

Final Answer:

• Nurse Evans should advise Mr. Clark that he can drink about 8.3 or 8 and 1/3 cups per day without exceeding his fluid restriction.

ANSWER: 8.3 or 8 and 1/3 cups

Simplified recap: Convert 2 liters (2000 mL) to cups using 1 cup = 240 mL. Dividing 2000 mL by 240 mL gives approximately 8.33 cups, which is about 8 and 1/3 cups.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Davis must administer 40 mg of furosemide IV push. The available medication is provided as 20 mg in 2 mL. We need to determine how many mL will deliver the ordered 40 mg.

Step-by-Step Calculation:

1. Determine the concentration:

• 20 mg is contained in 2 mL, so the concentration is 20 mg ÷ 2 mL = 10 mg/mL.

2. Calculate the required volume:

• Ordered dose = 40 mg.
• Volume required = 40 mg ÷ (10 mg/mL) = 4 mL.

Final Answer:

• Nurse Davis should prepare 4 mL to deliver the ordered dose of furosemide.

ANSWER: 4 mL

Simplified recap: The concentration is 10 mg/mL. Dividing 40 mg by 10 mg/mL gives 4 mL, which is the volume Nurse Davis should administer.

EXPLANATION

✔Solution:

Understanding the Problem:

Mr. Wilson is prescribed metoprolol tartrate 25 mg by mouth once daily. The pharmacy provided 50 mg scored tablets. The task is to determine how many tablets should be taken to provide a 25 mg dose.

Step-by-Step Calculation:

1. Identify the given values:

• Ordered dose: 25 mg
• Tablet strength: 50 mg per tablet

2. Set up the conversion using dimensional analysis:

Number of tablets = (Ordered dose) × (1 tablet / 50 mg)

3. Perform the calculation:

• 25 mg × (1 tablet / 50 mg) = 25/50 = 0.5 tablet

4. Final Answer:

• Nurse Miller should instruct Mr. Wilson to take 1/2 tablet daily.

ANSWER: 1/2 tablet

Simplified recap: Since 1 tablet contains 50 mg, a 25 mg dose is achieved by taking half of a tablet.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Bennett is to administer 50 mL of ceftriaxone in D5W over 20 minutes using an IV infusion controller. To program the pump, we need to convert the total volume and time into an infusion rate in milliliters per hour.

Step-by-Step Calculation:

1. Calculate the infusion rate in mL per minute:

• Total volume = 50 mL
• Total time = 20 minutes
• Infusion rate = 50 mL ÷ 20 minutes = 2.5 mL/min

2. Convert mL per minute to mL per hour:

• 2.5 mL/min × 60 minutes/hour = 150 mL/hour

Final Answer:

• Nurse Bennett should program the infusion controller to 150 mL/hour.

ANSWER: 150 mL/hour

Simplified recap: Divide 50 mL by 20 minutes to get 2.5 mL/min, then multiply by 60 to convert to 150 mL/hour.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Lee must manually regulate an aminophylline IV drip at 20 mL per hour using microdrip tubing. Microdrip tubing typically delivers 60 drops per mL. We need to calculate the drip rate in drops per minute (gtts/min).

Step-by-Step Calculation:

1. Convert the infusion rate from mL per hour to mL per minute:

• 20 mL/hour ÷ 60 minutes/hour = 0.333 mL/min

2. Convert the mL/min rate to drops per minute using the drop factor:

• 0.333 mL/min × 60 gtts/mL = 20 gtts/min

3. Final Answer:

• Nurse Lee should adjust the IV infusion to deliver 20 gtts/min.

ANSWER: 20 gtts/min

Simplified recap: 20 mL/hour equals 0.333 mL/min. Multiplying 0.333 mL/min by the microdrip drop factor (60 gtts/mL) yields 20 gtts/min.