NCLEX: Drug Dosage Calculation Exam 3

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Emily must administer 1,000,000 units of penicillin IM. The vial on hand contains 300,000 units per 1 mL. We need to figure out how many milliliters are required to reach a total of 1,000,000 units.

Step-by-Step Solution:

1. Key details:

• Ordered dose: 1,000,000 units of penicillin IM.
• Available concentration: 300,000 units per 1 mL.

2. Set up the calculation (dimensional analysis):

• 1,000,000 units ÷ (300,000 units / 1 mL) = 1,000,000 ÷ 300,000 mL.

3. Perform the division:

• 1,000,000 ÷ 300,000 = 3.33... mL
• Rounded to one decimal place is 3.3 mL.

4. Final volume to draw up:

• Nurse Emily should administer approximately 3.3 mL of penicillin.

ANSWER: 3.3 mL

Simplified recap: Divide the prescribed units (1,000,000) by the concentration in units per mL (300,000). This yields ~3.3 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Leo needs to administer 2,000 mL of normal saline over 4 hours. This is an IV rate calculation where you divide total volume (mL) by the total time (hours) to find the infusion rate in mL/hour.

Step-by-Step Solution:

1. Identify the total volume and time:

• Total volume: 2,000 mL of NS
• Total time: 4 hours

2. Use the basic formula:

Rate (mL/hour) = Total volume (mL) ÷ Time (hours)

3. Calculate the infusion rate:

• 2,000 mL ÷ 4 hours = 500 mL/hour

4. Confirm the result is reasonable:

• 500 mL/hour over 4 hours = 2,000 mL in total, matching the order.

ANSWER: 500 mL/hour

Simplified recap: Divide 2,000 mL by 4 hours to get 500 mL/hour.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Jordan needs to administer alprazolam (Xanax) 0.5 mg orally. The unit stock comes in 0.25 mg tablets. The objective is to determine how many 0.25 mg tablets equal a single 0.5 mg dose.

Step-by-Step Solution:

1. Identify the required dose and available strength:

• Prescribed dose: 0.5 mg
• Available tablet strength: 0.25 mg/tablet

2. Determine the number of tablets:

• Tablets needed = (Required dose) ÷ (Strength per tablet)
• = 0.5 mg ÷ 0.25 mg/tablet = 2 tablets

ANSWER: 2 tablets

Simplified recap: You need 0.5 mg total, each tablet is 0.25 mg, so two tablets provide 0.5 mg.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Devon must administer 400 mg of liquid erythromycin to a pediatric patient. The bottle label states 125 mg per 5 mL. The goal is to determine how many milliliters (mL) correspond to 400 mg.

Step-by-Step Solution:

1. Identify key details:

• Ordered dose: 400 mg erythromycin.
• Concentration on the label: 125 mg per 5 mL.

2. Determine the needed volume in mL (dimensional analysis):

• Start with the prescribed 400 mg.
• Use the ratio provided: 5 mL per 125 mg.

3. Set up and show crossing over of units:

400 mg × (5 mL ÷ 125 mg)

• “mg” cancels out, leaving the unit in mL.

4. Calculate the answer:

• Multiply numerator: 400 × 5 = 2000
• Divide by 125: 2000 ÷ 125 = 16

5. State the final volume:

• Nurse Devon should draw up 16 mL of the erythromycin solution.

ANSWER: 16 mL

Simplified recap: Multiply the dose ordered (400 mg) by the ratio of mL to mg (5 mL / 125 mg). After cancelling “mg,” the final result is 16 mL.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Tasha needs to infuse 2,000 mL of D5W over 24 hours, using manual IV tubing that has a drop factor of 15 gtt/mL. The goal is to calculate the drip rate (gtts/minute) to correctly set the manual flow regulator.

Step-by-Step Solution:

1. Identify key details:

• Total volume: 2,000 mL
• Time: 24 hours (24 × 60 = 1,440 minutes)
• Drop factor: 15 gtt/mL

2. Calculate the flow rate in mL/minute:

• Flow rate (mL/min) = Total volume (mL) ÷ Total time (minutes)
• = 2,000 mL ÷ 1,440 minutes ≈ 1.39 mL/min

3. Convert mL/min to gtt/min using the drop factor:

• Drip rate (gtt/min) = (mL/min) × (Drop factor in gtt/mL)
• = 1.39 mL/min × 15 gtt/mL ≈ 20.85 gtt/min
• Round to the nearest whole number ≈ 21 gtt/min

4. Final drip rate:

• Nurse Tasha should set approximately 21 gtts/minute.

ANSWER: 21 gtts/minute

Simplified recap: Divide total mL by total minutes (2,000 ÷ 1,440) to find mL/min. Then multiply by the drop factor (15 gtt/mL) to find gtt/min. Approximately 21 gtts/minute is needed.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Janelle needs to give her grandmother 10 mL of Maalox for indigestion. However, the grandmother only has standard household measuring tools (e.g., teaspoons). We must convert 10 mL to the equivalent amount in teaspoons.

Step-by-Step Solution:

1. Key conversion:

• 1 teaspoon (tsp) ≈ 5 mL

2. Find how many teaspoons in 10 mL:

• Total volume: 10 mL
• Divide by 5 mL/tsp: 10 mL ÷ 5 mL/tsp = 2 tsp

3. Final household measurement:

• 10 mL = 2 teaspoons

ANSWER: 2 teaspoons

Simplified recap: Since 1 teaspoon ≈ 5 mL, 10 mL is equal to 2 teaspoons.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Lila must administer 250 mg of erythromycin by mouth. The available tablet is labeled as 0.5 g (which equals 500 mg). The task is to figure out how many 500 mg tablets are needed to provide a 250 mg dose.

Step-by-Step Solution:

1. Convert the tablet strength to mg if needed:

• 0.5 g = 500 mg

2. Calculate how many tablets equal 250 mg:

• Tablet needed = (Ordered dose) ÷ (Tablet strength in mg)
• = 250 mg ÷ 500 mg/tablet = 0.5 tablet

3. Final dose to administer:

• Nurse Lila should give ½ tablet.

ANSWER: ½ tablet

Simplified recap: Since each tablet is 500 mg and the ordered dose is 250 mg, half of a 500 mg tablet will provide the required 250 mg.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Elena must help a patient mix didanosine (DDI) in liquid form. The prescription is for 200 mg by mouth twice daily, but the available powder packets each provide 167 mg. According to the instructions, one 167 mg powder packet is mixed with 4 ounces of water. The goal is to figure out how many total ounces of liquid the patient should mix to achieve a 200 mg dose.

Step-by-Step Solution:

1. Determine how many packets are needed for 200 mg:

• 200 mg required ÷ 167 mg per packet ≈ 1.20 packets

2. Convert that fraction of packets into fluid ounces needed:

• Each packet (167 mg) requires 4 oz of water.
• If 1 packet = 4 oz, then 1.20 packets = 1.20 × 4 oz = 4.8 oz.

3. Final mixing instruction:

• The patient should mix 4.8 oz of water with 1.20 packets to achieve a 200 mg dose.

ANSWER: 4.8 oz

Simplified recap: The patient needs slightly more than one packet (200 ÷ 167 = 1.20 packets). Since each packet must be mixed with 4 oz, multiply 1.20 by 4 oz to get 4.8 oz total.

EXPLANATION

✔Solution:

Understanding the Problem:

Nurse Omar must administer furosemide (Lasix) at a continuous rate of 2 mg/minute. The IV bag contains 400 mg of Lasix in 250 mL of D5W. We need to convert the ordered mg/minute into mg/hour, then figure out the correct mL/hour setting based on the concentration in the IV bag.

Step-by-Step Solution:

1. Convert the ordered dose to mg/hour:

• 2 mg/min × 60 min/hour = 120 mg/hour

2. Use the bag concentration to find mL/hour:

• The bag has 400 mg in 250 mL.
• We need 120 mg from that solution each hour.
• Set up the ratio: 400 mg is to 250 mL as 120 mg is to X mL.

3. Show crossing over of units (dimensional analysis):

120 mg / hour× (250 mL ÷ 400 mg)

• The “mg” cancels, leaving mL/hour.

4. Calculate:

• 120 × 250 = 30,000
• 30,000 ÷ 400 = 75 mL/hour

5. Final IV pump setting:

• Nurse Omar should set the controller to 75 mL/hour.

ANSWER: 75 mL/hour

Simplified recap: Convert 2 mg/min to 120 mg/hour. Since 400 mg are dissolved in 250 mL, multiply 120 mg by the ratio (250 mL / 400 mg). This equals 75 mL per hour.

EXPLANATION

✔Solution:

Understanding the Problem:

David is prescribed acetaminophen (Tylenol) in grain (gr) units: specifically, gr 15 every 6 hours. The safe upper limit of acetaminophen is 4 grams (4000 mg) per 24 hours. We need to determine how much total acetaminophen he receives in a 24-hour period, and compare that to the 4-gram safety threshold.

Step-by-Step Solution:

1. Recall the approximate conversion from grains to milligrams:

• 1 grain (gr) ≈ 60–65 mg.

2. Convert 15 grains to milligrams:

• If using 1 gr = 65 mg, then gr 15 ≈ 15 × 65 mg = 975 mg (≈ 1 g).
• If using 1 gr = 60 mg, then gr 15 ≈ 15 × 60 mg = 900 mg.

In many clinical references, 1 grain is rounded to 65 mg when dealing with acetaminophen, making gr 15 equal to approximately 975 mg—often interpreted as 1 g for simplicity.

3. Determine total doses per day:

• Every 6 hours means 4 doses per 24 hours.

4. Calculate total daily intake:

• If each dose is ~1 g (975 mg, often rounded up), then 4 doses in 24 hours = ~4 g total.

5. Compare to the safe upper limit:

• 4 g per day is the generally recognized maximum safe limit for most adults.
• Thus, David’s total daily acetaminophen intake is right at the 4-gram threshold.

ANSWER: 4 grams daily—right at the safe limit!

Simplified recap: Using the most common clinical convention of 1 grain ≈ 65 mg for acetaminophen, 15 grains ~ 1 g. Given every 6 hours (4 times/day) = ~4 g total, which matches the safe daily limit.