NCLEX: Drug Dosage Calculation Exam 4

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Emily must set an infusion rate for a continuous IV hydration order. The ordered fluid is 1 Liter of 5% Dextrose in 0.45% normal saline, which needs to be administered over 16 hours. To determine the infusion rate in mL per hour, we need to convert the total volume into milliliters and then divide by the time in hours.

Step-by-Step Solution:

1. Convert the total volume from Liters to milliliters:

• 1 Liter = 1000 mL

2. Set up the calculation (dimensional analysis) using the conversion:

1000 mL ÷ 16 hours

• Here, the "mL" remains in the numerator and "hours" in the denominator, giving the unit mL/hour.

3. Perform the calculation:

• 1000 mL ÷ 16 hours = 62.5 mL/hour
• This value rounds to approximately 63 mL/hour.

4. State the final infusion rate:

• Nurse Emily should set the infusion controller to 63 mL/hour.

ANSWER: 63 mL/hour

Simplified recap: Convert 1 Liter to 1000 mL, then divide by 16 hours (1000 mL ÷ 16 hours), resulting in approximately 62.5 mL/hour, which rounds to 63 mL/hour.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Fatima must administer a subcutaneous injection of heparin, with the order specifying 2500 units per injection. The available vial has a concentration of 5000 units per mL. The goal is to determine the correct volume (in mL) to draw up for 2500 units.

Step-by-Step Solution:

1. Identify the given values:

• Ordered dose: 2500 units
• Concentration: 5000 units/mL

2. Set up the conversion calculation using dimensional analysis:

2500 units × (1 mL / 5000 units)

• The units units cancel out, leaving mL.

3. Perform the calculation:

• 2500 ÷ 5000 = 0.5 mL

4. State the final volume:

• Nurse Fatima should prepare 0.5 mL of heparin for the injection.

ANSWER: 0.5 mL

Simplified recap: Multiply the ordered dose (2500 units) by the conversion factor (1 mL/5000 units). The "units" cancel out, yielding 0.5 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Carla must calculate the safe IV dose range of gentamicin for a patient weighing 190 pounds, based on a dosing recommendation of 1 to 5 mg per kilogram of body weight. This involves converting the weight from pounds to kilograms and then applying the dosing range.

Step-by-Step Solution:

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

• Conversion factor: 1 lb = 0.453592 kg
• Calculation with unit cancellation:

190 lb × (0.453592 kg / 1 lb) ≈ 86.18 kg

2. Apply the dosing range (1 to 5 mg/kg):

• Lower limit calculation:

1 mg/kg × 86.18 kg

→ Here, kg cancels out, leaving:

≈ 86.18 mg, which rounds to 86 mg

• Upper limit calculation:

5 mg/kg × 86.18 kg

→ Again, kg cancels out, leaving:

≈ 430.9 mg, which rounds to 431 mg

3. Determine the safe dose range:

• The safe IV dose range for gentamicin is approximately 86 mg to 431 mg.

ANSWER: 86 mg to 431 mg

Simplified recap: Convert 190 lb to approximately 86 kg using the conversion factor (cancelling the "lb" unit), then multiply by the dosing range (1 to 5 mg/kg) where the "kg" units cancel, resulting in a dose range of roughly 86 mg to 431 mg.

EXPLANATION

✔Solution:

Understanding the Problem:

Mrs. Gable needs to take 30 mL of a suspension, but she does not have a metric measuring device. Nurse Chris must convert the required 30 mL into a measure using a standard household tablespoon. It is known that one tablespoon is equivalent to 15 mL.

Step-by-Step Solution:

1. Identify the conversion factor:

• 1 tablespoon = 15 mL

2. Set up the conversion calculation using dimensional analysis:

30 mL × (1 tablespoon / 15 mL)

• The unit "mL" cancels out, leaving the measure in tablespoons.

3. Perform the calculation:

• 30 ÷ 15 = 2 tablespoons

4. State the final measurement:

• Nurse Chris should instruct Mrs. Gable to use two tablespoons to measure 30 mL.

ANSWER: Use two tablespoons.

Simplified recap: Multiply 30 mL by the conversion factor (1 tablespoon/15 mL). The mL units cancel, resulting in 2 tablespoons.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Reyes needs to administer heparin at a rate of 1000 units per hour. The available solution is a 250 mL bag containing 25,000 units of heparin. The task is to determine the infusion pump rate in mL per hour to achieve the ordered dosing.

Step-by-Step Solution:

1. Identify the given values:

• Ordered rate: 1000 units/hour
• Total volume of solution: 250 mL
• Total units in the solution: 25,000 units

2. Set up the conversion using dimensional analysis:

The conversion factor from units to mL is derived from the solution:

25,000 units in 250 mL → (250 mL / 25,000 units)

3. Calculate the infusion rate in mL per hour:

1000 units/hour × (250 mL / 25,000 units)

• The units cancel out:

1000 units/hour × (250 mL / 25,000 units)

• Simplify the calculation:

=(1000 × 250) ÷ 25,000 mL/hour

• Compute the numerator: 1000 × 250 = 250,000
• Divide: 250,000 ÷ 25,000 = 10 mL/hour

4. State the final infusion rate:

• Nurse Reyes should set the infusion pump to 10 mL/hour.

ANSWER: 10 mL/hour

Simplified recap: Multiply 1000 units/hour by the conversion factor (250 mL/25,000 units) with cancellation of "units" to yield 10 mL/hour.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Jordan must administer 1 Liter (1000 mL) of D5W over 8 hours using gravity tubing with a drop factor of 15 gtts/mL. The task is to determine the flow rate in drops per minute (gtts/min).

Step-by-Step Solution:

1. Convert the total volume to milliliters:

• 1 Liter = 1000 mL

2. Convert the total time from hours to minutes:

• 8 hours × 60 min/hour = 480 min

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

1000 mL ÷ 480 min = 2.0833 mL/min

• The "mL" unit remains, with "min" in the denominator.

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

2.0833 mL/min × (15 gtts / 1 mL)

≈ 31.25 gtts/min

• Rounding to the nearest whole number gives approximately 31 gtts/min.

ANSWER: 31 gtts/min

Simplified recap: Convert 1 Liter to 1000 mL and 8 hours to 480 minutes. Divide 1000 mL by 480 min to get 2.0833 mL/min. Multiply by the drop factor (15 gtts/mL) with cancellation of "mL" to yield about 31 gtts/min.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Ben has recorded several sources of fluid intake over an 8-hour shift. The fluids include beverages measured in ounces or cups, and an IV infusion measured in milliliters (mL). The goal is to convert all the volumes to mL and sum them to obtain the total fluid intake.

Step-by-Step Solution:

1. Convert the volumes measured in cups and ounces to milliliters (mL):

• Standard conversion: 1 cup = 8 oz = 240 mL
• 1 oz: 1 oz = 240 mL ÷ 8 = 30 mL

2. List and convert each fluid source:

• Coffee: Three 8-oz cupsCalculation: 3 cups × 240 mL/cup = 720 mL(8 oz in each cup cancels with conversion factor yielding mL)
• Orange juice: 4 oz. Calculation: 4 oz × 30 mL/oz = 120 mL(oz cancels, leaving mL)
• Milk: Three-quarters (0.75) of a cup. Calculation: 0.75 cup × 240 mL/cup = 180 mL
• Tomato soup: One 8-oz bowl. Calculation: 8 oz × 30 mL/oz = 240 mL
• Jell-O: Half a cup. Calculation: 0.5 cup × 240 mL/cup = 120 mL
• Water: Two cups. Calculation: 2 cups × 240 mL/cup = 480 mL
• IV infusion: 750 mL. No conversion needed.

3. Sum all the converted volumes:

Total fluid intake = 720 mL (coffee) + 120 mL (orange juice) + 180 mL (milk) + 240 mL (tomato soup) + 120 mL (Jell-O) + 480 mL (water) + 750 mL (IV infusion)

• Step-by-step addition:720 + 120 = 840 mL

  840 + 180 = 1020 mL

  1020 + 240 = 1260 mL

  1260 + 120 = 1380 mL

  1380 + 480 = 1860 mL

  1860 + 750 = 2610 mL

4. Final Answer:

• Nurse Ben should record a total fluid intake of 2610 mL for the 8-hour period.

ANSWER: 2,610 mL intake

Simplified recap: Convert all fluid volumes to mL (using 1 cup = 240 mL and 1 oz = 30 mL), then add: 720 + 120 + 180 + 240 + 120 + 480 + 750 = 2610 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

The physician ordered codeine grain 1/4 for intramuscular injection. The available ampule is labeled as codeine grain 1/2 per mL. Nurse Ella must determine how many milliliters are needed to deliver the ordered dose of grain 1/4.

Step-by-Step Solution:

1. Identify the given values:

• Ordered dose: grain 1/4
• Available concentration: grain 1/2 per mL

2. Set up the conversion calculation using dimensional analysis:

Ordered dose = grain 1/4

Available concentration = grain 1/2 per 1 mL

To find the required volume, set up the calculation as:

grain 1/4 × (1 mL / grain 1/2)

• The unit grain cancels out, leaving the answer in mL.

3. Perform the calculation:

• Divide the fractions: (1/4) ÷ (1/2) = (1/4) × (2/1) = 2/4 = 1/2

This means that Nurse Ella should administer 0.5 mL of codeine.

ANSWER: 0.5 mL

Simplified recap: Convert the ordered dose (grain 1/4) using the available concentration (grain 1/2 per mL) by setting up the ratio: 1/4 × (1 mL/1/2). With the cancellation of the "grain" unit, the calculation simplifies to 1/2 mL, which equals 0.5 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Reyes must administer 250,000 units of penicillin G via intramuscular injection. The available vial has a concentration of 300,000 units per milliliter. The goal is to determine the volume (in mL) required to provide the ordered 250,000 units.

Step-by-Step Solution:

1. Identify the given values:

• Ordered dose: 250,000 units
• Concentration: 300,000 units per 1 mL

2. Set up the conversion calculation using dimensional analysis:

250,000 units × (1 mL / 300,000 units)

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

3. Perform the calculation:

• 250,000 ÷ 300,000 = 0.8333 mL, which rounds to approximately 0.8 mL

4. State the final volume:

• Nurse Reyes should draw up 0.8 mL of the penicillin G solution.

ANSWER: 0.8 mL

Simplified recap: Multiply 250,000 units by the conversion factor (1 mL/300,000 units). The "units" cancel out, yielding approximately 0.8333 mL, which rounds to 0.8 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Anya must infuse 50 mL of gatifloxacin diluted in D5W over 30 minutes using gravity infusion tubing with a drop factor of 10 gtts/mL. The goal is to determine the correct flow rate in drops per minute (gtts/min).

Step-by-Step Solution:

1. Identify the given values:

• Total volume: 50 mL
• Total time: 30 minutes
• Drop factor: 10 gtts/mL

2. Calculate the infusion rate in mL per minute:

50 mL ÷ 30 min = 1.67 mL/min

• Here, the unit "mL" remains and "min" is in the denominator.

3. Convert the infusion rate to drops per minute (gtts/min) using the drop factor:

1.67 mL/min × (10 gtts / 1 mL)

→ The mL cancels out, leaving:

≈ 16.67 gtts/min

• When rounded to the nearest whole number, this is approximately 17 gtts/min.

4. State the final flow rate:

• Nurse Anya should regulate the flow rate to 17 gtts/min to ensure the medication infuses over 30 minutes.

ANSWER: 17 gtts/min

Simplified recap: Divide 50 mL by 30 minutes to obtain 1.67 mL/min, then multiply by the drop factor (10 gtts/mL). With cancellation of the mL units, the result is about 16.67 gtts/min, which rounds to 17 gtts/min.