NCLEX: Drug Dosage Calculation Exam 1

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Kai is to administer 1 mg of lorazepam by mouth. The available tablets are 0.5 mg each. We need to determine how many tablets will provide a 1 mg dose.

Step-by-Step Calculation:

1. Identify the given values:

• Ordered dose: 1 mg
• Tablet strength: 0.5 mg per tablet

2. Set up the conversion:

Number of tablets = 1 mg × (1 tablet / 0.5 mg)

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

3. Perform the calculation:

• 1 mg ÷ 0.5 mg/tablet = 2 tablets

Final Answer:

• Nurse Kai should administer 2 tablets of lorazepam.

ANSWER: 2 tablets

Simplified recap: Dividing the ordered dose (1 mg) by the tablet strength (0.5 mg per tablet) yields 2 tablets.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Caleb must administer 40 mg of methadone subcutaneously. The available vial is labeled as 30 mg per 1 mL. The goal is to determine how many mL are needed to provide 40 mg.

Step-by-Step Calculation:

1. Identify the given values:

• Ordered dose: 40 mg
• Concentration: 30 mg per 1 mL

2. Set up the conversion using dimensional analysis:

Volume required = 40 mg × (1 mL / 30 mg)

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

3. Perform the calculation:

• 40 mg ÷ 30 mg/mL ≈ 1.33 mL

Final Answer:

• Nurse Caleb should draw up approximately 1.33 mL for this dose.

ANSWER: 1.33 mL

Simplified recap: Dividing the ordered dose (40 mg) by the concentration (30 mg/mL) yields about 1.33 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Janelle needs to administer 160 mg of methylprednisolone IM. The medication is supplied in vials labeled as 125 mg per 2 mL. We need to calculate the volume (in mL) that contains 160 mg.

Step-by-Step Calculation:

1. Identify the given values:

• Ordered dose: 160 mg
• Concentration: 125 mg per 2 mL

2. Set up the conversion using dimensional analysis:

Volume required = 160 mg × (2 mL / 125 mg)

• The “mg” units cancel, leaving mL.

3. Perform the calculation:

• Multiply: 160 × 2 = 320
• Divide: 320 ÷ 125 = 2.56 mL

4. Final Answer:

• Nurse Janelle should draw up 2.56 mL for a single dose.

ANSWER: 2.56 mL

Simplified recap: Multiply 160 mg by the conversion factor (2 mL/125 mg) to obtain 2.56 mL, with the mg units canceling out.

EXPLANATION

✔Solution:

Understanding the Problem:

The patient is ordered to take 400,000 units of oral nystatin every 4 hours by swishing and swallowing. The available solution has a concentration of 100,000 units per 5 mL. We need to determine the volume in mL required for 400,000 units and then convert that volume into teaspoons using household measuring spoons.

Step-by-Step Calculation:

1. Determine the volume (in mL) needed for 400,000 units:

• Since 100,000 units are contained in 5 mL, then:
• Volume required = (400,000 units ÷ 100,000 units) × 5 mL = 4 × 5 mL = 20 mL

2. Convert milliliters to teaspoons:

• Standard conversion: 1 teaspoon = 5 mL
• Thus, 20 mL ÷ 5 mL/teaspoon = 4 teaspoons

Final Answer:

• The patient should take 4 teaspoons per dose.

ANSWER: 4 teaspoons

Simplified recap: To deliver 400,000 units, 20 mL is required (since 100,000 units/5 mL), which converts to 4 teaspoons because 1 teaspoon is 5 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

The patient is prescribed 650 mg of acetaminophen by mouth, four times a day. The liquid form provided has a concentration of 160 mg per 5 mL. We need to calculate the volume in mL that contains 650 mg.

Step-by-Step Calculation:

1. Identify the given values:

• Ordered dose: 650 mg
• Concentration: 160 mg per 5 mL

2. Set up the conversion using dimensional analysis:

Volume (mL) = 650 mg × (5 mL / 160 mg)

• The "mg" units cancel, leaving mL.

3. Perform the calculation:

• 650 × 5 = 3250
• 3250 ÷ 160 ≈ 20.31 mL

4. Rounding:

• This value rounds to approximately 20 mL.

Final Answer:

• The patient should take 20 mL with each dose.

ANSWER: 20 mL

Simplified recap: Multiply 650 mg by (5 mL/160 mg) to get approximately 20.31 mL, which rounds to 20 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

The patient is prescribed a methadone dose of 15 mg per day by mouth. The oral solution is supplied as 10 mg in 5 mL. We need to calculate the volume in mL that contains 15 mg of methadone.

Step-by-Step Calculation:

1. Determine the concentration of the solution:

• 10 mg is in 5 mL, so the concentration is: 10 mg ÷ 5 mL = 2 mg/mL

2. Calculate the required volume for 15 mg:

• Volume (mL) = Dose (mg) ÷ Concentration (mg/mL)
• Volume = 15 mg ÷ 2 mg/mL = 7.5 mL

Final Answer:

• The nurse should instruct the patient to take 7.5 mL of the methadone oral solution.

ANSWER: 7.5 mL

Simplified recap: With a concentration of 2 mg/mL, dividing 15 mg by 2 mg/mL gives 7.5 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Liana must administer a daily dose of digoxin 0.25 mg by mouth. The available tablets are 0.125 mg each. We need to calculate how many tablets are required to provide the 0.25 mg dose.

Step-by-Step Calculation:

1. Identify the given values:

• Ordered dose: 0.25 mg
• Tablet strength: 0.125 mg per tablet

2. Set up the conversion using dimensional analysis:

Number of tablets = 0.25 mg × (1 tablet / 0.125 mg)

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

3. Perform the calculation:

• 0.25 ÷ 0.125 = 2 tablets

Final Answer:

• Nurse Liana should administer 2 tablets of digoxin.

ANSWER: 2 tablets

Simplified recap: Dividing the ordered dose (0.25 mg) by the tablet strength (0.125 mg) yields 2 tablets.

EXPLANATION

✔Solution:

Understanding the Problem:

Mr. Campbell (the patient) is restricted to 1000 mL of fluid per day. We need to total the fluid intake from all sources (beverages and water taken with medications) to determine if he exceeded his daily limit.

Step-by-Step Calculation:

1. Convert standard measurements:

• 1 cup ≈ 240 mL
• 1 oz ≈ 30 mL

2. Calculate fluid intake for each meal and medications:

• Breakfast:
  • 1 cup of coffee = 240 mL
  • 3 oz of milk = 3 × 30 = 90 mL
  • Total = 240 mL + 90 mL = 330 mL
• Lunch:
  • 6 oz lemonade = 6 × 30 = 180 mL
  • 1 cup of soup = 240 mL
  • Total = 180 mL + 240 mL = 420 mL
• Supper:
  • 1 cup of coffee = 240 mL
• Medications:
  • Morning water: 4 oz = 4 × 30 = 120 mL
  • Evening water: 4 oz = 120 mL
  • Total = 120 mL + 120 mL = 240 mL

3. Total Daily Fluid Intake:

• Breakfast: 330 mL
• Lunch: 420 mL
• Supper: 240 mL
• Medications: 240 mL

Total = 330 + 420 + 240 + 240 = 1230 mL

4. Compare with the Restriction:

• Daily limit = 1000 mL
• Total consumed = 1230 mL, which exceeds the limit.

Final Answer:

• Yes, the patient exceeded his daily fluid allowance.

Simplified recap: Converting cups and ounces to mL, the total fluid intake is 1230 mL, which is above the 1000 mL limit.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse David must administer 45 mg of codeine via IM injection. The available vial is labeled as 60 mg per 2 mL, which indicates the concentration of the medication.

Step-by-Step Calculation:

1. Determine the concentration in mg per mL:

• 60 mg is contained in 2 mL, so the concentration is:

60 mg ÷ 2 mL = 30 mg/mL

2. Calculate the volume required to provide 45 mg:

• Volume (mL) = Ordered dose (mg) ÷ Concentration (mg/mL)
• Volume = 45 mg ÷ 30 mg/mL = 1.5 mL

Final Answer:

• Nurse David should draw up 1.5 mL for the injection.

ANSWER: 1.5 mL

Simplified recap: The vial's concentration is 30 mg/mL, so dividing the ordered dose (45 mg) by 30 mg/mL yields 1.5 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Priya must administer a weight-based IM dose of hydromorphone at 0.015 mg/kg for a patient weighing 150 pounds. The available vial is labeled 4 mg/mL. We first convert the patient’s weight to kilograms, calculate the required dose in mg, and then determine the volume (in mL) needed from the available concentration.

Step-by-Step Calculation:

1. Convert weight from pounds to kilograms:

• 1 lb ≈ 0.4536 kg
• 150 lb × 0.4536 kg/lb ≈ 68.04 kg

2. Calculate the ordered dose in mg:

• Ordered dose = 0.015 mg/kg × 68.04 kg ≈ 1.0206 mg

3. Determine the volume to administer using the concentration:

• Concentration = 4 mg/mL
• Volume required = Dose ÷ Concentration = 1.0206 mg ÷ 4 mg/mL ≈ 0.25515 mL

4. Rounding:

• Rounded to two decimal places, the volume is approximately 0.26 mL.

Final Answer:

• Nurse Priya should administer 0.26 mL of hydromorphone.

ANSWER: 0.26 mL

Simplified recap: Convert 150 lb to about 68 kg, multiply by 0.015 mg/kg to get approximately 1.02 mg, and divide by 4 mg/mL to yield about 0.26 mL.