NCLEX: Drug Dosage Calculation Exam 6

EXPLANATION

✔Solution:

Understanding the Problem:

Mr. Diaz is prescribed acetaminophen 325 mg, two tablets by mouth every 6 hours for pain. To determine the total daily dosage in grams, we need to calculate the dose per administration, the number of administrations per day, and then convert the total milligrams to grams.

Step-by-Step Solution:

1. Calculate the dose per administration:

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

2. Determine the number of doses per day:

• The dose is given every 6 hours.
• There are 24 hours in a day: 24 ÷ 6 = 4 doses per day.

3. Calculate the total daily dose in mg:

• Total daily dose = 650 mg/dose × 4 doses = 2600 mg.

4. Convert the total daily dose from milligrams to grams:

• 1 gram = 1000 mg.
• 2600 mg ÷ 1000 = 2.6 g.

Final Answer:

• Mr. Diaz is receiving a total daily dose of 2.6 g of acetaminophen.

ANSWER: 2.6 g

Simplified recap: Two 325 mg tablets equal 650 mg per dose; given every 6 hours (4 times per day), the total daily dose is 650 mg × 4 = 2600 mg, which converts to 2.6 g.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Evelyn's patient weighs 120 pounds and is prescribed vancomycin IVPB 500 mg every 6 hours. To determine the daily dosage in mg/kg, we first convert the patient's weight from pounds to kilograms, calculate the total daily dose, and then divide by the weight in kg. The maximum safe daily dose is 40 mg/kg, so we will also assess if the current order is within safe limits.

Step-by-Step Solution:

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

• 120 lb × (0.453592 kg / 1 lb) ≈ 54.43 kg

2. Calculate the total daily dose:

• Dose per administration = 500 mg
• Frequency = every 6 hours → 4 doses/day
• Total daily dose = 500 mg × 4 = 2000 mg/day

3. Determine the daily dose in mg/kg:

• Daily dose per kg = Total daily dose ÷ Weight in kg
• 2000 mg ÷ 54.43 kg ≈ 36.7 mg/kg

4. Compare with the maximum safe daily dose:

• Maximum safe dose = 40 mg/kg
• Calculated dose = 36.7 mg/kg, which is within safe limits.

ANSWER: The patient is prescribed a daily dose of 36.7 mg/kg.

Simplified recap: Convert 120 lb to approximately 54.43 kg, calculate the total daily dose (2000 mg), then divide 2000 mg by 54.43 kg to get about 36.7 mg/kg, which is below the 40 mg/kg maximum.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Rodriguez must manually infuse 350 mL of packed red blood cells over 2 hours using tubing with a drop factor of 10 gtts/mL. The goal is to calculate the flow rate in drops per minute (gtts/min).

Step-by-Step Solution:

1. Convert the total infusion time to minutes:

• 2 hours × 60 minutes/hour = 120 minutes

2. Calculate the infusion rate in mL per minute:

350 mL ÷ 120 minutes ≈ 2.92 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:

2.92 mL/min × (10 gtts / 1 mL)

→ The mL cancels out, leaving:

≈ 29.2 gtts/min

• Rounded to the nearest whole number, the rate is approximately 29 gtts/min.

4. Final Answer:

• Nurse Rodriguez should set the infusion at 29 gtts/min.

ANSWER: 29 gtts/minute

Simplified recap: Convert 2 hours to 120 minutes, then divide 350 mL by 120 minutes to obtain about 2.92 mL/min. Multiply by the drop factor (10 gtts/mL) to get approximately 29.2 gtts/min, which rounds to 29 gtts/min.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Sarah must administer 40 mg of diphenhydramine hydrochloride intramuscularly. The available injection has a concentration of 25 mg per mL. The task is to determine the volume in mL needed to deliver the prescribed 40 mg dose.

Step-by-Step Solution:

1. Identify the given values:

• Ordered dose: 40 mg
• Concentration: 25 mg per 1 mL

2. Set up the conversion using dimensional analysis:

Volume required = 40 mg × (1 mL / 25 mg)

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

3. Perform the calculation:

• 40 ÷ 25 = 1.6 mL

4. Final Answer:

• Nurse Sarah should prepare 1.6 mL of the diphenhydramine hydrochloride solution.

ANSWER: 1.6 mL

Simplified recap: Divide the ordered dose (40 mg) by the concentration (25 mg/mL) to obtain 1.6 mL, with the mg units canceling appropriately.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Reyes is to administer an IV piggyback infusion of fosphenytoin. The order is for 100 phenytoin equivalents (PE) per dose, and the medication comes in 50 mL of normal saline. The vial label instructs that the infusion should not exceed 150 PE per minute. We need to calculate the maximum infusion rate in mL per hour based on this limit.

Step-by-Step Solution:

1. Determine the concentration of the solution:

• Ordered dose (per infusion): 100 PE is diluted in 50 mL.
• Concentration = 100 PE ÷ 50 mL = 2 PE/mL

2. Calculate the maximum allowable volume per minute based on the rate limit:

• Maximum infusion rate allowed = 150 PE/min.
• Using the concentration, convert PE/min to mL/min:
  Volume (mL/min) = (150 PE/min) × (1 mL / 2 PE)

  → 150 ÷ 2 = 75 mL/min

  Here, the unit PE cancels out.

3. Convert the rate from mL per minute to mL per hour:

• 75 mL/min × 60 min/hour = 4500 mL/hour

4. Final Answer:

• Nurse Reyes should program the infusion pump to a maximum rate of 4500 mL/hour.

ANSWER: 4,500 mL/hour maximum rate.

Simplified recap: The concentration is 2 PE/mL (100 PE/50 mL). Dividing the maximum allowed 150 PE/min by 2 PE/mL gives 75 mL/min, which when multiplied by 60 minutes equals 4500 mL/hour.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Fatima must infuse 1000 mL of normal saline over a period of 6 hours using an electronic infusion pump. The goal is to determine the rate in milliliters per hour (mL/hr) that the pump should be set to deliver the entire volume in the prescribed time.

Step-by-Step Solution:

1. Identify the given values:

• Total Volume: 1000 mL
• Total Time: 6 hours

2. Set up the calculation using dimensional analysis:

Infusion rate = Total Volume ÷ Total Time

1000 mL ÷ 6 hours

• Here, the mL remains and the "hours" is in the denominator, yielding mL/hour.

3. Perform the calculation:

• 1000 ÷ 6 ≈ 166.67 mL/hour
• Rounded to the nearest whole number, this is approximately 167 mL/hour.

4. Final Answer:

• Nurse Fatima should program the pump to deliver at a rate of 167 mL/hour.

ANSWER: 167 mL/hour

Simplified recap: Divide 1000 mL by 6 hours (1000 mL ÷ 6 hours = 166.67 mL/hour, which rounds to 167 mL/hour).

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Thompson is to administer 500 mL of D5W containing corticotropin over 8 hours using an infusion controller. Even though the order includes 25 Units of corticotropin, the pump is programmed based on the total volume to be infused. We must calculate the infusion rate in mL per hour.

Step-by-Step Solution:

1. Identify the given values:

• Total volume: 500 mL
• Total time: 8 hours

2. Set up the calculation using dimensional analysis:

Infusion rate = Total volume ÷ Total time

500 mL ÷ 8 hours

• The mL units remain and "hours" is in the denominator, yielding mL/hour.

3. Perform the calculation:

• 500 ÷ 8 = 62.5 mL/hour
• This value rounds to approximately 63 mL/hour

4. Final Answer:

• Nurse Thompson should program the infusion controller to 63 mL/hour.

ANSWER: 63 mL/hour

Simplified recap: Divide 500 mL by 8 hours (500 mL ÷ 8 hours = 62.5 mL/hour, which rounds to 63 mL/hour).

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Ana must administer 100 mL of ceftizoxime in dextrose 5% in water over 30 minutes as an IV piggyback infusion, using gravity drip tubing with a drop factor of 10 gtts/mL. The task is to calculate the infusion rate in drops per minute (gtts/min).

Step-by-Step Solution:

1. Identify the given values:

• Total volume: 100 mL
• Total time: 30 minutes
• Drop factor: 10 gtts/mL

2. Calculate the infusion rate in mL per minute using dimensional analysis:

100 mL ÷ 30 min = 3.33 mL/min

3. Convert the rate to drops per minute (gtts/min):

3.33 mL/min × (10 gtts / 1 mL)

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

3.33 × 10 = 33.33 gtts/min, which rounds to approximately 33 gtts/min.

4. Final Answer:

• Nurse Ana should regulate the infusion at 33 gtts/min.

ANSWER: 33 gtts/min

Simplified recap: Divide 100 mL by 30 minutes to get 3.33 mL/min, then multiply by the drop factor (10 gtts/mL) to yield about 33.33 gtts/min, which rounds to 33 gtts/min.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Emily must administer 0.375 mg of digoxin. The available tablets each contain 0.25 mg of digoxin. The goal is to determine how many tablets are needed to achieve the prescribed dose.

Step-by-Step Solution:

1. Identify the given values:

• Ordered dose: 0.375 mg digoxin
• Tablet strength: 0.25 mg per tablet

2. Set up the conversion using dimensional analysis:

Number of tablets = 0.375 mg × (1 tablet / 0.25 mg)

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

3. Perform the calculation:

• 0.375 ÷ 0.25 = 1.5 tablets

4. Final Answer:

• Nurse Emily should administer 1.5 tablets of digoxin.

ANSWER: 1.5 tablets

Simplified recap: Divide the ordered dose (0.375 mg) by the tablet strength (0.25 mg per tablet) to obtain 1.5 tablets, with the mg units cancelling appropriately.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Jackson must administer 500 mL of lipids as a piggyback infusion over a 24-hour period. The task is to calculate the infusion rate in milliliters per hour (mL/hr) so that the entire 500 mL is infused over 24 hours.

Step-by-Step Solution:

1. Identify the given values:

• Total volume: 500 mL
• Total time: 24 hours

2. Set up the calculation using dimensional analysis:

Infusion rate = Total Volume ÷ Total Time

500 mL ÷ 24 hours

3. Perform the calculation:

• 500 ÷ 24 ≈ 20.83 mL/hour

4. Rounding:

• 20.83 mL/hour rounds to approximately 21 mL/hour

5. Final Answer:

• Nurse Jackson should program the infusion pump to 21 mL/hour.

ANSWER: 21 mL/hour

Simplified recap: Divide 500 mL by 24 hours (500 mL ÷ 24 hours ≈ 20.83 mL/hour, which rounds to 21 mL/hour).