NCLEX: Drug Dosage Calculation Exam 2

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Jackson needs to administer methylprednisolone 60 mg IM. The medication on hand contains 75 mg per 1 mL. We must determine how many milliliters (mL) will provide the required 60 mg dose.

Step-by-Step Solution:

1. Key details:

• Ordered dose: 60 mg of methylprednisolone, IM.
• Available concentration: 75 mg per 1 mL.

2. Identify what is required:

• The volume in mL that corresponds to 60 mg.

3. Set up dimensional analysis:

• Start with the ordered dose (60 mg).
• Use the concentration from the vial (1 mL / 75 mg).

4. Show multiplication and cancel units:

60 mg × (1 mL ÷ 75 mg)

• "mg" cancels out, leaving mL.

5. Solve the calculation:

• 60 ÷ 75 = 0.8 mL

6. Final volume to administer:

• Nurse Jackson should draw up 0.8 mL of the medication.

ANSWER: 0.8 mL

Simplified recap: Multiply the ordered dose (60 mg) by the vial’s ratio (1 mL / 75 mg). After cancellation, the answer is 0.8 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Mia needs to administer 50 mg of ranitidine (Zantac) in 50 mL D5W over 30 minutes. The drip factor (also called the drop factor) of the IV tubing is 15 gtts/mL (drops per milliliter). The goal is to calculate how many drops per minute (gtts/minute) the infusion should run at to complete in 30 minutes.

Step-by-Step Solution:

1. Key information:

• Total volume: 50 mL
• Time to infuse: 30 minutes
• Drip factor: 15 gtts/mL

2. Formula for drops per minute:

gtts/minute = (Total volume [mL] × Drop factor [gtts/mL]) ÷ Time [minutes]

3. Plug in the values:

gtts/minute = (50 mL × 15 gtts/mL) ÷ 30 min

4. Perform the multiplication and division:

• 50 × 15 = 750
• 750 ÷ 30 = 25

5. Final drops per minute calculation:

• Nurse Mia should run the infusion at 25 gtts/minute.

ANSWER: 25 gtts/minute

Simplified recap: Multiply the total volume by the drop factor, then divide by the total infusion time. (50 mL × 15 gtts/mL) ÷ 30 min = 25 gtts/minute.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Isabel must administer 15 mg of morphine intramuscularly (IM). The vial on hand has a concentration of 10 mg per 1 mL. The goal is to determine how many milliliters are needed to deliver 15 mg.

Step-by-Step Solution:

1. Key details:

• Ordered dose: 15 mg of morphine.
• Available concentration: 10 mg per 1 mL.

2. Convert the ordered dose to mL (dimensional analysis):

• 15 mg ÷ (10 mg/mL) = 1.5 mL

3. Final volume:

• Nurse Isabel will administer 1.5 mL.

ANSWER: 1.5 mL

Simplified recap: Divide the required dose (15 mg) by the concentration (10 mg per mL) to get 1.5 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Olivia must administer meperidine (also known as Demerol) at a dose of 75 mg intramuscularly (IM). The vial on hand contains meperidine at a concentration of 50 mg per 1 mL. The goal is to determine the volume in milliliters (mL) needed to provide 75 mg.

Step-by-Step Solution:

1. Key details:

• Ordered dose: 75 mg of meperidine, IM.
• Available concentration: 50 mg per 1 mL.

2. What needs to be found:

• The volume (mL) that corresponds to 75 mg of meperidine.

3. Set up the dimensional analysis:

• Begin with the ordered dose (75 mg).
• Use the ratio from the vial: 1 mL per 50 mg.

4. Show multiplication and unit cancellation:

75 mg × (1 mL ÷ 50 mg)

• The unit "mg" cancels out, leaving mL.

5. Solve for mL:

• 75 × 1 = 75
• 75 ÷ 50 = 1.5 mL

6. Final volume required:

• Nurse Olivia should draw up 1.5 mL of the meperidine solution.

ANSWER: 1.5 mL

Simplified recap: Multiply the prescribed dose (75 mg) by the ratio (1 mL / 50 mg) to get 1.5 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Elaine has an order to give 12,000 units of heparin subcutaneously (SC). The available vial indicates that the medication concentration is 5,000 units per 1 mL. The task is to figure out how many milliliters (mL) Nurse Elaine must administer to provide 12,000 units.

Step-by-Step Solution:

1. Identify key points:

• Ordered dose: 12,000 units heparin (SC).
• Available concentration: 5,000 units per 1 mL.

2. Determine the required volume in mL:

• We need to convert units (of heparin) to mL using the concentration on the vial.

3. Set up the dimensional analysis calculation:

• Begin with 12,000 units (the ordered amount).
• Use the vial's ratio: 1 mL / 5,000 units.

4. Show the multiplication and cancel units:

12,000 units × (1 mL ÷ 5,000 units)

• The "units" cancel, leaving mL as the unit for the answer.

5. Solve for the volume:

• 12,000 × 1 = 12,000
• 12,000 ÷ 5,000 = 2.4 mL

6. Final required volume:

• Nurse Elaine should administer 2.4 mL to provide 12,000 units.

ANSWER: 2.4 mL of the heparin solution

Simplified recap: By multiplying the prescribed dose (12,000 units) by the ratio of mL per unit (1 mL/5,000 units), the volume needed is 2.4 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Priya needs to set an IV heparin infusion at 700 units per hour for Mrs. Lewis. The IV solution concentration is 100 units per 1 mL. The goal is to determine how many milliliters per hour (mL/hour) must be administered to achieve the target of 700 units/hour.

Step-by-Step Solution:

1. Identify key details:

• Desired rate: 700 units/hour of heparin.
• Concentration on hand: 100 units per 1 mL of IV solution.

2. Determine what needs to be calculated:

• The IV pump setting in mL/hour.

3. Set up the dimensional analysis:

• Use the desired dose (700 units/hour).
• Convert from units to mL using the available concentration (1 mL / 100 units).

4. Show the multiplication and cancel units:

700 units per hour × (1 mL ÷ 100 units)

• The "units" cancel out, leaving mL/hour as the final unit.

5. Solve for mL/hour:

• 700 ÷ 100 = 7

6. Final infusion rate setting:

• Nurse Priya should set the IV pump to 7 mL/hour.

ANSWER: 7 mL/hour

Simplified recap: Multiply 700 units/hour by 1 mL/100 units. After unit cancellation, the pump setting is 7 mL/hour.

EXPLANATION

✔Solution:

1. Convert the ordered dose from grains to milligrams:

• 1 grain (gr) is commonly approximated as 60 mg.
• Ordered dose: gr 1/150 = 1/150 × 60 mg = 0.4 mg.

2. Determine the volume to administer based on the available concentration:

• Available atropine: 0.4 mg/mL.
• Needed dose: 0.4 mg.

3. Set up the dimensional analysis:

• 0.4 mg (ordered) × (1 mL / 0.4 mg) = 1 mL.

4. Conclude the volume in mL:

• Nurse Harris should administer 1 mL of the atropine solution.

ANSWER: 1 mL of the atropine solution.

Explanation: Using the conversion 1 grain ≈ 60 mg, the dose of gr 1/150 equals 0.4 mg. With the vial labeled 0.4 mg per 1 mL, the nurse needs 1 mL to deliver the correct 0.4 mg dose.

EXPLANATION

✔Solution:

Understanding the Problem:

Mrs. Patel needs to mix her oral potassium supplement with 120 mL of fluid, but she only has standard kitchen measuring cups at home. A typical U.S. measuring cup holds about 240 mL (8 fluid ounces). We need to figure out which fraction of a cup corresponds to 120 mL.

Step-by-Step Solution:

1. Recognize the standard cup volume:

• 1 cup ≈ 240 mL

2. Determine the fraction of a cup that is 120 mL:

• 120 mL is half of 240 mL.
• So, 120 mL = ½ cup.

3. Confirm the conversion:

• ½ cup = 240 mL ÷ 2 = 120 mL.

ANSWER: ½ cup

Simplified recap: Since 1 cup is about 240 mL, half that amount (½ cup) equals 120 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Lucas must provide 1000 mg of acetaminophen orally (as an elixir). The available elixir concentration is 160 mg for every 5 mL. The objective is to find how many milliliters of this elixir are needed to deliver a 1000 mg dose.

Step-by-Step Solution:

1. Gather the key information:

• Ordered dose: 1000 mg acetaminophen.
• Elixir concentration: 160 mg per 5 mL.

2. Identify what must be calculated:

• The volume (in mL) that corresponds to 1000 mg based on the given concentration.

3. Set up the dimensional analysis:

• Start with the ordered 1000 mg.
• Use the ratio from the bottle: (5 mL / 160 mg).

4. Show the multiplication and cancel out units:

1000 mg × (5 mL ÷ 160 mg)

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

5. Compute the dose in mL:

• Multiply numerator: 1000 × 5 = 5000
• Divide by 160: 5000 ÷ 160 = 31.25 mL

6. Final volume to administer:

• Nurse Lucas should administer 31.25 mL of the elixir.

ANSWER: 31.25 mL

Simplified recap: Multiply the prescribed dose (1000 mg) by the ratio of mL per mg (5 mL / 160 mg). After canceling the mg unit, the result is 31.25 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Mr. Foster has a 24-hour fluid restriction of 1000 mL. Nurse Elena needs to calculate how much fluid he has already consumed during her 12-hour shift (7 a.m. to 7 p.m.) so she can determine how much fluid remains for the night shift (7 p.m. to 7 a.m.).

Step-by-Step Solution:

1. Identify daily fluid limit and consumption period:

• Total fluid limit (24 hours): 1000 mL
• Day shift (7 a.m. – 7 p.m.): Nurse Elena’s shift
• Night shift (7 p.m. – 7 a.m.): Remainder of 24-hour period

2. Calculate fluid intake during the day shift:

• Coffee intake: Three meals, each with ½ cup (120 mL).
  • 3 × 120 mL = 360 mL
• Water with medications: 50 mL at 7 a.m., noon, and 5 p.m.
  • 3 × 50 mL = 150 mL
• Soda intake: 240 mL

Total day shift intake: 360 mL + 150 mL + 240 mL = 750 mL

3. Subtract day shift intake from the 24-hour limit:

• 1000 mL (24-hour limit) – 750 mL (day shift use) = 250 mL left

4. Final answer (fluid allowance for night shift):

• Mr. Foster can have 250 mL from 7 p.m. to 7 a.m.

ANSWER: 250 mL

Simplified recap: Add up all fluids consumed during 7 a.m. to 7 p.m. (coffee, water with meds, soda), then subtract from the total 24-hour limit. The remainder is what can be used for 7 p.m. to 7 a.m.