NCLEX: Drug Dosage Calculation Exam 5

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Reyes must administer amphotericin B at a dose of 0.5 mg/kg once daily. The patient weighs 236 pounds, so the first step is to convert the weight from pounds to kilograms. Then, using the prescribed dose, we calculate the total daily dose in milligrams.

Step-by-Step Solution:

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

• Conversion factor: 1 lb = 0.453592 kg
• Calculation:

236 lb × (0.453592 kg / 1 lb) ≈ 107.1 kg

2. Apply the dosing range (0.5 mg/kg):

• Dose = 0.5 mg/kg × 107.1 kg

0.5 mg/kg × 107.1 kg = 53.55 mg

3. Round the result:

• 53.55 mg rounds to approximately 53.6 mg

4. Final Answer:

• Nurse Reyes should administer approximately 53.6 mg of amphotericin B each day.

ANSWER: 53.6 mg

Simplified recap: Convert 236 lb to 107.1 kg (using 1 lb = 0.453592 kg) and multiply by the dose of 0.5 mg/kg. The kg units cancel, yielding approximately 53.6 mg.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Katrina needs to administer a dose of morphine 4 mg IV push. The available ampule is labeled as grain 1/6 per mL. Since the order is in mg, we first need to convert the concentration from grains to mg. (Note: 1 grain is equivalent to 64.8 mg.)

Step-by-Step Solution:

1. Convert the available concentration to mg per mL:

• Available concentration: grain 1/6 per mL
• Convert 1/6 grain to mg:      1/6 grain × (64.8 mg / 1 grain)

  → The unit grain cancels out, leaving:

  64.8 mg ÷ 6 = 10.8 mg/mL

2. Calculate the required volume to deliver 4 mg:

• Ordered dose: 4 mg
• Volume (mL) = Ordered dose ÷ Concentration      → 4 mg × (1 mL / 10.8 mg)

  → The unit mg cancels out, leaving:

  4 ÷ 10.8 ≈ 0.37 mL

3. Rounding:

• 0.37 mL rounds to approximately 0.4 mL

4. Final Answer:

• Nurse Katrina should prepare 0.4 mL of morphine.

ANSWER: 0.4 mL

Simplified recap: Convert the available concentration from 1/6 grain per mL to mg per mL using the conversion (1 grain = 64.8 mg) to get 10.8 mg/mL. Then, divide the ordered dose (4 mg) by 10.8 mg/mL to obtain approximately 0.37 mL, which rounds to 0.4 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Paolo must administer an intramuscular injection of morphine with a prescribed dose of 15 mg. The available vial is labeled as grain 1/4 per mL, meaning that each mL contains 1/4 grain of morphine. Since the order is in mg, we must first convert the concentration from grains to mg, then determine the volume needed.

Step-by-Step Solution:

1. Convert the available concentration to mg per mL:

• Conversion factor: 1 grain = 64.8 mg
• Calculation: (1/4 grain/mL) × (64.8 mg/1 grain)
  → The unit grain cancels out, leaving:

  64.8 mg ÷ 4 = 16.2 mg/mL

2. Determine the required volume to deliver 15 mg:

• Ordered dose = 15 mg
• Volume required = (15 mg) × (1 mL / 16.2 mg)
  → The unit mg cancels out, resulting in:

  15 ÷ 16.2 ≈ 0.93 mL

3. Rounding:

• Approximately 0.93 mL rounds to 1 mL

4. Final Answer:

• Nurse Paolo should prepare 1 mL of the morphine solution.

ANSWER: 1 mL

Simplified recap: Convert the available concentration from 1/4 grain per mL to mg by multiplying 1/4 by 64.8 mg (yielding 16.2 mg/mL). Then, divide the ordered dose (15 mg) by 16.2 mg/mL, resulting in approximately 0.93 mL, which rounds to 1 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Reyes must administer 80 mg of furosemide IV. The available vial is labeled as furosemide 20 mg in 2 mL. The task is to calculate the volume of this solution needed to provide the prescribed 80 mg dose.

Step-by-Step Solution:

1. Identify the given values:

• Ordered dose: 80 mg of furosemide
• Available concentration: 20 mg in 2 mL

2. Determine the concentration in mg per mL:

20 mg in 2 mL can be expressed as:

20 mg ÷ 2 mL = 10 mg/mL

3. Set up the conversion using dimensional analysis:

Volume required = (Ordered dose) ÷ (Concentration)

80 mg × (1 mL / 10 mg)

• The mg cancels out, leaving the volume in mL.

4. Perform the calculation:

• 80 ÷ 10 = 8 mL

5. Final Answer:

• Nurse Reyes should prepare 8 mL of the furosemide solution to deliver the prescribed dose.

ANSWER: 8 mL

Simplified recap: The available solution has a concentration of 10 mg/mL (20 mg in 2 mL). Dividing the ordered dose (80 mg) by 10 mg/mL yields 8 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Ana must administer a stat dose of phenobarbital 160 mg intravenously. The available concentration is 60 mg per mL. The goal is to calculate the volume in mL needed to deliver 160 mg.

Step-by-Step Solution:

1. Identify the given values:

• Ordered dose: 160 mg
• Available concentration: 60 mg per 1 mL

2. Set up the conversion calculation using dimensional analysis:

160 mg × (1 mL / 60 mg)

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

3. Perform the calculation:

• Divide: 160 ÷ 60 ≈ 2.6667 mL
• Rounded to the nearest tenth, this is approximately 2.7 mL

4. State the final volume:

• Nurse Ana should draw up 2.7 mL of phenobarbital to administer the ordered dose.

ANSWER: 2.7 mL

Simplified recap: Multiply 160 mg by the conversion factor (1 mL/60 mg) with cancellation of "mg", resulting in approximately 2.67 mL, which rounds to 2.7 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Maria must administer 500 mL of normal saline over 4 hours using gravity infusion tubing with a drop factor of 10 gtts/mL. The goal is to determine the flow rate in drops per minute (gtts/min).

Step-by-Step Solution:

1. Convert the infusion time to minutes:

• 4 hours × 60 minutes/hour = 240 minutes

2. Calculate the infusion rate in mL per minute:

500 mL ÷ 240 minutes = 2.0833 mL/min

• The unit "mL" remains in the numerator, while "minutes" is in the denominator.

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

2.0833 mL/min × (10 gtts / 1 mL)

→ Here, the mL cancels out, leaving:

≈ 20.833 gtts/min

• Rounding to the nearest whole number gives approximately 21 gtts/min.

4. Final Answer:

• Nurse Maria should regulate the flow at 21 gtts/min.

ANSWER: 21 gtts/min

Simplified recap: Convert 4 hours to 240 minutes, then divide 500 mL by 240 minutes to get 2.0833 mL/min. Multiply by 10 gtts/mL (with the mL units cancelling) to yield approximately 21 gtts/min.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Emily must administer an oral dose of levothyroxine 0.05 mg once daily. The available tablet is 0.1 mg per tablet. The goal is to determine the number of tablets needed to provide 0.05 mg.

Step-by-Step Solution:

1. Identify the given values:

• Ordered dose: 0.05 mg
• Tablet strength: 0.1 mg per tablet

2. Set up the conversion using dimensional analysis:

Number of tablets = (Ordered dose) × (1 tablet / 0.1 mg)

• The mg units cancel out, leaving the answer in tablets.

3. Perform the calculation:

• 0.05 mg × (1 tablet / 0.1 mg) = 0.05 / 0.1 = 0.5 tablet

4. Final Answer:

• Nurse Emily should prepare 1/2 tablet of levothyroxine to deliver the prescribed dose.

ANSWER: 1/2 tablet

Simplified recap: Divide the ordered dose (0.05 mg) by the tablet strength (0.1 mg per tablet). The "mg" units cancel out, resulting in 0.5 tablet, which is equivalent to 1/2 tablet.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Grace must administer an oral dose of furosemide 40 mg. The available tablets contain 20 mg each. The task is to determine how many tablets are needed to achieve the ordered 40 mg dose.

Step-by-Step Solution:

1. Identify the given values:

• Ordered dose: 40 mg
• Tablet strength: 20 mg per tablet

2. Set up the conversion using dimensional analysis:

Number of tablets = (Ordered dose) ÷ (Tablet strength)

40 mg × (1 tablet / 20 mg)

• The mg units cancel out, leaving the result in tablets.

3. Perform the calculation:

• 40 ÷ 20 = 2 tablets

4. Final Answer:

• Nurse Grace should administer 2 tablets of furosemide.

ANSWER: 2 tablets

Simplified recap: Divide the ordered dose (40 mg) by the tablet strength (20 mg per tablet) to obtain 2 tablets.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Lei is to infuse 100 mL of cefuroxime in dextrose 5% in water over 60 minutes. The task is to calculate the flow rate in drops per minute using gravity tubing with a drop factor of 10 gtts/mL.

Step-by-Step Solution:

1. Convert the infusion time to minutes:

• Time = 60 minutes

2. Calculate the infusion rate in mL per minute:

100 mL ÷ 60 minutes = 1.667 mL/min

• The unit "mL" remains in the numerator while "minutes" is in the denominator.

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

1.667 mL/min × (10 gtts / 1 mL)

• The mL cancels out, leaving the unit in gtts/min.

1.667 × 10 = 16.67 gtts/min

• Rounded to the nearest whole number, the rate is approximately 17 gtts/min.

4. Final Answer:

• Nurse Lei should set the infusion at 17 gtts/min.

ANSWER: 17 gtts/min

Simplified recap: Divide 100 mL by 60 minutes to obtain 1.667 mL/min, then multiply by 10 gtts/mL. The "mL" units cancel, resulting in approximately 16.67 gtts/min, which rounds to 17 gtts/min.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Ben must administer a subcutaneous injection of heparin at a dose of 3000 units. The available vial contains 5000 units per mL. The task is to calculate the volume (in mL) needed to deliver 3000 units.

Step-by-Step Solution:

1. Identify the given values:

• Ordered dose: 3000 units
• Available concentration: 5000 units per 1 mL

2. Set up the conversion calculation using dimensional analysis:

3000 units × (1 mL / 5000 units)

• The units cancel out, leaving the result in mL.

3. Perform the calculation:

• 3000 ÷ 5000 = 0.6 mL

4. Final Answer:

• Nurse Ben should prepare 0.6 mL of heparin for the injection.

ANSWER: 0.6 mL

Simplified recap: Divide the ordered dose (3000 units) by the concentration (5000 units/mL) using the conversion factor (1 mL/5000 units). The "units" cancel out, yielding 0.6 mL.