NCLEX: Drug Dosage Calculation Exam 7

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Reyes must administer 0.6 mg of atropine intramuscularly. The available solution is labeled as 0.4 mg per mL. To determine the correct volume to administer, we use the given concentration to convert the ordered dose into milliliters.

Step-by-Step Solution:

1. Identify the given values:

• Ordered dose: 0.6 mg
• Concentration: 0.4 mg per mL

2. Set up the conversion using dimensional analysis:

Volume required = 0.6 mg × (1 mL / 0.4 mg)

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

3. Perform the calculation:

• 0.6 ÷ 0.4 = 1.5 mL

4. Final Answer:

• Nurse Reyes should administer 1.5 mL of the atropine solution.

ANSWER: 1.5 mL

Simplified recap: Divide the ordered dose (0.6 mg) by the concentration (0.4 mg/mL) to obtain 1.5 mL, with the "mg" units canceling out.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Reyes must administer enoxaparin subcutaneously at a dose of 1 mg/kg. The patient weighs 200 pounds, and the available enoxaparin is in a prefilled syringe labeled 30 mg per 0.3 mL. We need to convert the patient's weight to kilograms, calculate the required dose in mg, and then determine the volume to be administered using the given concentration.

Step-by-Step Solution:

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

• Conversion factor: 1 lb = 0.453592 kg
• Calculation: 200 lb × (0.453592 kg / 1 lb) ≈ 90.7 kg

2. Calculate the required dose in mg:

• Dose = 1 mg/kg × 90.7 kg = 90.7 mg

3. Determine the concentration of the enoxaparin solution:

• The label indicates 30 mg per 0.3 mL.
• This is equivalent to: 30 mg ÷ 0.3 mL = 100 mg/mL

4. Set up the conversion using dimensional analysis:

Volume required = 90.7 mg × (0.3 mL / 30 mg)

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

5. Perform the calculation:

• 90.7 mg ÷ 30 mg = 3.0233
• Then, 3.0233 × 0.3 mL = 0.907 mL (approximately)

6. Rounding:

• 0.907 mL rounds to approximately 0.9 mL

Final Answer:

• Nurse Reyes should administer 0.9 mL of the enoxaparin solution.

ANSWER: 0.9 mL

Simplified recap: Convert 200 lb to approximately 90.7 kg, then calculate the dose as 90.7 mg (1 mg/kg). Using the concentration (30 mg in 0.3 mL), set up the ratio 90.7 mg × (0.3 mL/30 mg) to yield approximately 0.9 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Reyes must administer 90 mg of diltiazem per dose. The available tablets are 60 mg each and are scored, which allows them to be split if necessary. The goal is to determine how many tablets are needed to provide the ordered 90 mg dose.

Step-by-Step Solution:

1. Identify the given values:

• Ordered dose: 90 mg
• Tablet strength: 60 mg per tablet

2. Set up the conversion using dimensional analysis:

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

90 mg × (1 tablet / 60 mg)

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

3. Perform the calculation:

• 90 ÷ 60 = 1.5 tablets

4. Final Answer:

• Nurse Reyes should administer 1.5 tablets of diltiazem for each dose.

ANSWER: 1.5 tablets

Simplified recap: Divide the ordered dose (90 mg) by the tablet strength (60 mg per tablet). The calculation (90 ÷ 60) results in 1.5 tablets.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Thomas must determine the number of levothyroxine tablets to give a patient and check whether the dose is within the safe daily range. The provider ordered 150 mcg of levothyroxine daily. The pharmacy supplies tablets of 0.075 mg each, and the patient weighs 196 pounds. The safe daily range is 1.5 mcg/kg.

Step-by-Step Calculation:

1. Convert the tablet strength to micrograms:

• 0.075 mg per tablet × (1000 mcg / 1 mg) = 75 mcg per tablet

2. Determine the number of tablets needed:

• Ordered dose = 150 mcg
• Number of tablets = 150 mcg ÷ 75 mcg per tablet = 2 tablets

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

• 1 lb = 0.453592 kg
• 196 lb × 0.453592 kg/lb ≈ 88.9 kg

4. Calculate the dose per kilogram:

• Dose per kg = Total dose ÷ Weight in kg
• 150 mcg ÷ 88.9 kg ≈ 1.6875 mcg/kg, which rounds to approximately 1.7 mcg/kg

5. Evaluate Safety:

• The safe daily range is 1.5 mcg/kg. Since 1.7 mcg/kg exceeds 1.5 mcg/kg, the dose is not safe.

Final Answer:

• Nurse Thomas calculates that 2 tablets are needed, but the patient is receiving approximately 1.7 mcg/kg, which is above the safe limit.

ANSWER: 2 tablets. The patient is receiving 1.7 mcg/kg. Not safe!

Simplified recap: Each 0.075 mg tablet equals 75 mcg, so 150 mcg requires 2 tablets. Converting 196 lb to 88.9 kg yields a dose of 150 mcg ÷ 88.9 kg ≈ 1.7 mcg/kg, which exceeds the safe limit of 1.5 mcg/kg.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Serena's patient is prescribed Tylenol #3, which consists of 2 tablets every 4 hours. Each tablet contains 325 mg of acetaminophen. We need to verify that the total daily acetaminophen intake does not exceed the safe limit of 4 grams (4000 mg).

Step-by-Step Calculation:

1. Calculate the acetaminophen per dose:

• Each tablet = 325 mg
• 2 tablets per dose: 2 × 325 mg = 650 mg per dose

2. Determine the number of doses per day:

• Dosing every 4 hours means: 24 hours ÷ 4 hours/dose = 6 doses per day

3. Calculate the total daily dose:

• Total daily dose = 650 mg/dose × 6 doses = 3900 mg
• Convert to grams: 3900 mg ÷ 1000 = 3.9 grams

4. Compare with the safe daily limit:

• The safe limit is 4 grams per day. Since 3.9 grams is below 4 grams, the dosage is safe.

ANSWER: 3.9 grams per day. Safe!

Simplified recap: Each dose is 2 tablets (650 mg), with 6 doses daily totaling 3900 mg (or 3.9 g), which is within the safe limit of 4 grams per day.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse dela Cruz needs to administer 180 mg of amoxicillin per dose to a pediatric patient. The available suspension is labeled 125 mg per 5 mL. We must calculate the volume (in mL) that contains 180 mg of amoxicillin.

Step-by-Step Solution:

1. Identify the given values:

• Ordered dose: 180 mg
• Available concentration: 125 mg per 5 mL

2. Set up the conversion using dimensional analysis with cancellation:

180 mg × (5 mL / 125 mg)

• The unit mg cancels out, leaving mL.

3. Perform the calculation:

• Multiply: 180 × 5 = 900
• Divide: 900 ÷ 125 = 7.2 mL

4. Final Answer:

• Nurse dela Cruz should administer 7.2 mL of the amoxicillin suspension for each dose.

ANSWER: 7.2 mL

Simplified recap: The calculation is 180 mg × (5 mL / 125 mg) = 7.2 mL, with the "mg" units canceling, yielding the correct volume in mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Santos must administer 2 mg of morphine sulfate via IV push. The available morphine is supplied as grain 1/6 per mL. To calculate the volume in mL required, we first need to convert the concentration from grains to mg, then determine how many mL provide 2 mg.

Step-by-Step Solution:

1. Convert the concentration from grains to mg per mL:

• Conversion factor: 1 grain = 64.8 mg
• Given concentration = 1/6 grain/mL
• Calculation: (1/6 grain/mL) × (64.8 mg/1 grain)→ 64.8 mg ÷ 6 = 10.8 mg/mL
  
  Here, the unit grain cancels out.

2. Determine the required volume to deliver 2 mg:

• Ordered dose = 2 mg
• Using the conversion factor:Volume required = 2 mg × (1 mL / 10.8 mg)

  → The mg units cancel out, yielding:

  2 ÷ 10.8 ≈ 0.185 mL

3. Rounding:

• 0.185 mL rounds to approximately 0.2 mL

4. Final Answer:

• Nurse Santos should administer approximately 0.2 mL of the morphine sulfate injection.

ANSWER: 0.2 mL

Simplified recap: Convert the concentration (1/6 grain/mL) to mg/mL using 1 grain = 64.8 mg, yielding 10.8 mg/mL. Then, divide the ordered dose (2 mg) by 10.8 mg/mL to get about 0.185 mL, which rounds to 0.2 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Aquino must administer heparin sodium at a rate of 1000 units per hour. The available solution contains 50,000 units in 500 mL of 5% Dextrose in Water. We need to determine the infusion rate in mL per hour that will deliver 1000 units per hour.

Step-by-Step Solution:

1. Determine the concentration of the solution:

• Concentration = 50,000 units ÷ 500 mL = 100 units/mL

2. Set up the conversion using dimensional analysis with cancellation:

1000 units/hour × (1 mL / 100 units)

• The "units" cancel out, leaving:

1000 ÷ 100 = 10 mL/hour

3. Final Answer:

• Nurse Aquino should program the infusion pump to 10 mL/hour.

ANSWER: 10 mL/hour

Simplified recap: The concentration of the heparin solution is 100 units/mL. Dividing the ordered rate (1000 units/hour) by 100 units/mL gives 10 mL/hour.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Reyes must infuse 100 mL of cefazolin in 5% Dextrose over 20 minutes. To program the infusion pump, we need to convert this rate to milliliters per hour.

Step-by-Step Solution:

1. Identify the given values:

• Total volume: 100 mL
• Total time: 20 minutes

2. Calculate the infusion rate in mL per minute:

• Infusion rate = 100 mL ÷ 20 minutes = 5 mL/min

3. Convert mL per minute to mL per hour:

• 5 mL/min × 60 minutes/hour = 300 mL/hour

4. Final Answer:

• Nurse Reyes should program the infusion pump at 300 mL/hour.

ANSWER: 300 mL/hour

Simplified recap: Divide 100 mL by 20 minutes to get 5 mL/min. Multiplying 5 mL/min by 60 minutes yields 300 mL/hour.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Isabella must infuse 250 mL of normal saline over 4 hours using gravity IV 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 total infusion time to minutes:

• 4 hours × 60 minutes/hour = 240 minutes

2. Calculate the infusion rate in mL per minute:

• Infusion rate = Total volume ÷ Total time
• 250 mL ÷ 240 minutes ≈ 1.04 mL/min

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

• 1.04 mL/min × (10 gtts / 1 mL)→ The mL cancels out, yielding:

  ≈ 10.4 gtts/min

4. Rounding:

• 10.4 gtts/min rounds to approximately 10 gtts/min.

Final Answer:

• Nurse Isabella should regulate the IV flow at 10 gtts/min.

ANSWER: 10 gtts/minute

Simplified recap: Convert 4 hours to 240 minutes, then calculate the infusion rate (250 mL ÷ 240 min ≈ 1.04 mL/min). Multiplying by the drop factor (10 gtts/mL) gives approximately 10.4 gtts/min, which rounds to 10 gtts/min.