NEX Mathematical Calculations: Dosages and Solutions 2 — Questions and Answers

Question 1: A physician orders 500 mg of amoxicillin. The available supply is 250 mg per capsule. How many capsules should the nurse administer?

1 capsule
2 capsules (Correct answer)
3 capsules
4 capsules

Correct answer: 2 capsules

Using the formula: Desired dose / Available dose = 500 mg / 250 mg = 2 capsules.

The basic dosage calculation formula is: Number of doses = Desired (ordered) dose ÷ Available (on hand) dose. In this case: 500 mg ÷ 250 mg per capsule = 2 capsules. This is one of the most fundamental calculations in nursing pharmacology. Always verify the units match (both in mg) before calculating. After calculation, apply the reasonableness test: 2 capsules is a standard dose that a patient can safely swallow. If the calculation had yielded an unusually large number (e.g., 10 capsules), it would warrant double-checking the order and available supply. Nurses should always use the three checks (right patient, right drug, right dose, right route, right time) when administering medications.

Question 2: A patient weighs 176 pounds. A medication is ordered at 5 mg/kg/day divided into two doses. What is the amount per dose?

100 mg
200 mg (Correct answer)
400 mg
440 mg

Correct answer: 200 mg

Convert pounds to kg: 176 ÷ 2.2 = 80 kg. Total daily dose: 80 × 5 = 400 mg. Divided by 2 doses: 400 ÷ 2 = 200 mg per dose.

Weight-based dosage calculations require multiple steps: (1) Convert weight to kilograms: 176 lbs ÷ 2.2 = 80 kg. (2) Calculate total daily dose: 80 kg × 5 mg/kg/day = 400 mg/day. (3) Divide by number of doses: 400 mg ÷ 2 = 200 mg per dose. This type of calculation is extremely common in nursing, especially in pediatrics where all doses are weight-based. Always convert pounds to kilograms first (1 kg = 2.2 lbs). Common errors include forgetting to divide by the number of doses per day or using the wrong conversion factor. Double-checking with dimensional analysis can verify the answer: 176 lbs × (1 kg/2.2 lbs) × (5 mg/1 kg/day) × (1 day/2 doses) = 200 mg/dose.

Question 3: An IV infusion of 1,000 mL of normal saline is ordered to run over 8 hours. The drip factor is 15 gtt/mL. What is the correct flow rate in gtt/min?

21 gtt/min
25 gtt/min
31 gtt/min (Correct answer)
42 gtt/min

Correct answer: 31 gtt/min

Flow rate = (Volume × Drop factor) / (Time in minutes) = (1000 × 15) / (8 × 60) = 15000 / 480 = 31.25, rounded to 31 gtt/min.

The IV flow rate formula is: gtt/min = (Total volume in mL × Drop factor in gtt/mL) ÷ (Total time in minutes). Step by step: (1) Total volume = 1,000 mL. (2) Drop factor = 15 gtt/mL. (3) Time = 8 hours × 60 min/hour = 480 minutes. (4) Calculation: (1,000 × 15) ÷ 480 = 15,000 ÷ 480 = 31.25 gtt/min, rounded to 31 gtt/min. Common drip factors are 10, 15, and 20 gtt/mL for macrodrip sets and 60 gtt/mL for microdrip sets. When using a microdrip set, the flow rate in gtt/min equals the flow rate in mL/hour. Nurses must be able to calculate and regulate flow rates manually in case electronic infusion pumps malfunction.

Question 4: How many milliliters of a drug should be drawn up if the order is for 75 mg and the vial contains 100 mg/2 mL?

0.75 mL
1.0 mL
1.5 mL (Correct answer)
2.0 mL

Correct answer: 1.5 mL

Using the formula: (Desired/Available) × Volume = (75/100) × 2 = 0.75 × 2 = 1.5 mL.

The dosage calculation formula for liquid medications is: Volume to administer = (Desired dose ÷ Available dose) × Volume on hand. Calculation: (75 mg ÷ 100 mg) × 2 mL = 0.75 × 2 mL = 1.5 mL. Alternatively, using ratio-proportion: 100 mg/2 mL = 75 mg/x mL → 100x = 150 → x = 1.5 mL. Or using dimensional analysis: 75 mg × (2 mL/100 mg) = 1.5 mL. All three methods yield the same answer. When drawing up injectable medications, use an appropriate syringe size (a 3 mL syringe for 1.5 mL), ensure the correct concentration is used if multiple concentrations are available, and verify the route of administration (IM, SubQ, or IV).

Question 5: A nurse needs to prepare a 1:4 dilution of a stock solution. If the final volume needed is 200 mL, how much stock solution is required?

25 mL
40 mL
50 mL (Correct answer)
80 mL

Correct answer: 50 mL

A 1:4 dilution means 1 part stock to a total of 4 parts. Stock volume = Total volume / Dilution factor = 200 / 4 = 50 mL of stock solution.

Dilution ratios express the relationship between the concentrated substance and the total volume. A 1:4 dilution means 1 part stock solution in 4 total parts (1 part stock + 3 parts diluent). To find the stock volume: Stock = Total volume ÷ Total parts = 200 mL ÷ 4 = 50 mL. The diluent volume would be: 200 - 50 = 150 mL. Important distinction: 1:4 means 1 part IN 4 total (not 1 part stock + 4 parts diluent, which would be 1:5 total). In nursing, dilutions are used for preparing solutions for wound irrigation, mixing medications, and creating cleaning solutions. Always clarify whether a ratio refers to parts of total or parts of diluent, as this difference significantly affects concentration.

Question 6: A patient receives heparin at 1,200 units/hour. The IV bag contains 25,000 units in 500 mL. What is the infusion rate in mL/hour?

12 mL/hr
20 mL/hr
24 mL/hr (Correct answer)
48 mL/hr

Correct answer: 24 mL/hr

First find the concentration: 25,000 units / 500 mL = 50 units/mL. Then: 1,200 units/hr ÷ 50 units/mL = 24 mL/hr.

Heparin drip calculations are among the most critical in nursing. Step 1: Determine the concentration: 25,000 units ÷ 500 mL = 50 units/mL. Step 2: Calculate the infusion rate: 1,200 units/hr ÷ 50 units/mL = 24 mL/hr. Using dimensional analysis: 1,200 units/hr × (500 mL/25,000 units) = 600,000/25,000 = 24 mL/hr. Heparin is a high-alert medication that requires independent double-checks by two nurses, continuous infusion pump use, and regular aPTT monitoring. The nurse must verify both the concentration calculation and the pump rate. Common heparin concentrations include 25,000 units/250 mL and 25,000 units/500 mL. Incorrect calculations can lead to dangerous bleeding or inadequate anticoagulation.

NEX Mathematical Calculations: Dosages and Solutions 2

A physician orders 500 mg of amoxicillin.
The available supply is 250 mg per capsule.
How many capsules should the nurse administer?