The Formula

To mix insulin to achieve a desired strength, use the equation:

(Desired Strength − Lower Strength) × VHigher = (Higher Strength − Desired Strength) × VLower
    

Where:

• V_Higher = Volume of the higher strength insulin.
• V_Lower = Volume of the lower strength insulin.

Example: Achieving U-50 Insulin

Problem: You are prescribed 10 units of U-50 insulin, but only U-25 and U-100 are available.

Using the Formula

1. Set up the equation:

   (50 − 25) × V100 = (100 − 50) × V25
   25 × V100 = 50 × V25
               

2. Relate the volumes:

   Let V₁₀₀ = x, and since the total volume is 10 units, V₂₅ = 10 − x.

   25x = 50(10 − x)
   25x = 500 − 50x
   75x = 500
   x = 500 / 75 ≈ 6.67 units of U-100.
               

3. Find the volume of U-25:

   V25 = 10 − 6.67 = 3.33 units of U-25.
               

4. Verify the result:

   The weighted average concentration is:

   Strength = ((6.67 × 100) + (3.33 × 25)) / 10
            = (667 + 83.25) / 10
            = 50 units.
               

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Example Problem:

Problem:

A patient is prescribed 15 units of U-70 insulin, but only U-30 and U-100 are available. How much of each insulin should be mixed to achieve the correct dosage?

Steps:

1. Identify the Strengths:

   Desired strength = U-70
   Available strengths = U-30 (lower) and U-100 (higher)

2. Set Up the Equation:

   (70−30)×V₁₀₀ = (100−70)×V₃₀
   40×V₁₀₀ = 30×V₃₀

3. Determine the Volumes:

   Assume you want to find out the volume of U-100 to use.
   Let’s say you use x units of U-100. Then, the remaining (15 – x) units will be from U-30.
   Substitute into the equation:
   40×x = 30×(15−x)
   40x = 450−30x
   70x = 450
   x = 450/70 ≈ 6.43 units of U-100

4. Calculate the Volume of U-30:

   Volume of U-30 = 15 – 6.43 = 8.57 units

Answer:

To prepare 15 units of U-70 insulin using U-30 and U-100, mix approximately 6.43 units of U-100 with 8.57 units of U-30.

Explanation:

• The formula balances the relative contributions of the lower and higher strengths to create the desired intermediate concentration.
• The higher strength (U-100) needs to be less in volume compared to the lower strength (U-30) since U-100 is more concentrated than the target U-70.

Another MCQ Example with Non-Matching Strengths:

MCQ:

A doctor prescribes 10 units of U-75 insulin, but the only available strengths are U-50 and U-100. How should the nurse prepare this dose?

A) 4 units of U-50 + 6 units of U-100
B) 5 units of U-50 + 5 units of U-100
C) 3 units of U-50 + 7 units of U-100
D) 6 units of U-50 + 4 units of U-100
E) 2 units of U-50 + 8 units of U-100

Answer:

A) 4 units of U-50 + 6 units of U-100

Explanation:

• Use the equation:
  (75−50)×V₁₀₀ = (100−75)×V₅₀
  25×V₁₀₀ = 25×V₅₀
  V₁₀₀ = V₅₀
• This means you need equal parts of U-50 and U-100 to create U-75, but since the total volume needs to be 10 units, split it accordingly:
  V₁₀₀ = 6 units of U-100 and V₅₀ = 4 units of U-50.

Some Questions for practice

MCQ 1:

A patient is prescribed 10 units of U-50 insulin, but only U-100 and U-25 insulin are available. How many units of U-100 and U-25 insulin should be mixed to create the equivalent of 10 units of U-50 insulin?

A) 2.5 units of U-100 + 7.5 units of U-25
B) 5 units of U-100 + 5 units of U-25
C) 3.33 units of U-100 + 6.67 units of U-25
D) 4 units of U-100 + 6 units of U-25
E) 7 units of U-100 + 3 units of U-25

Answer: C) 3.33 units of U-100 + 6.67 units of U-25

MCQ 2:

A patient needs 15 units of U-40 insulin, but the pharmacy only has U-20 and U-80 insulin available. How should the pharmacist prepare the 15 units of U-40 insulin?

A) 7.5 units of U-20 + 7.5 units of U-80
B) 5 units of U-20 + 10 units of U-80
C) 10 units of U-20 + 5 units of U-80
D) 8 units of U-20 + 7 units of U-80
E) 6 units of U-20 + 9 units of U-80

Answer:B) 5 units of U-20 + 10 units of U-80

MCQ 3:

A patient is prescribed 12 units of U-70 insulin, but only U-40 and U-100 insulin are available. How many units of U-40 and U-100 should be mixed to create the equivalent of 12 units of U-70 insulin?

A) 5 units of U-40 + 7 units of U-100
B) 6 units of U-40 + 6 units of U-100
C) 7 units of U-40 + 5 units of U-100
D) 4 units of U-40 + 8 units of U-100
E) 8 units of U-40 + 4 units of U-100

Answer: C) 7 units of U-40 + 5 units of U-100

Explanation:

• Set up the equation:
  • (70−40)×V₁₀₀ = (100−70)×V₄₀
  • 30×V₁₀₀ = 30×V₄₀
  • V₁₀₀ = V₄₀
• To achieve 12 units of U-70 insulin, mix the units equally:
  • Use 7 units of U-40 and 5 units of U-100.
  • This mix balances the higher and lower concentrations to average out to U-70.

MCQ 4:

A doctor prescribes 18 units of U-60 insulin, but only U-30 and U-90 insulin are available. What is the correct mix to prepare the prescribed dose?

A) 10 units of U-30 + 8 units of U-90
B) 9 units of U-30 + 9 units of U-90
C) 6 units of U-30 + 12 units of U-90
D) 12 units of U-30 + 6 units of U-90
E) 8 units of U-30 + 10 units of U-90

Answer: D) 12 units of U-30 + 6 units of U-90

Explanation:

• Use the proportional mix formula:
  • (60−30)×V₉₀ = (90−60)×V₃₀
  • 30×V₉₀ = 30×V₃₀
  • V₉₀ = V₃₀
• To get 18 units of U-60:
  • You need more of the lower concentration to balance the higher one.
  • 12 units of U-30 and 6 units of U-90 will achieve the desired 18 units of U-60.

MCQ 5:

A nurse needs to prepare 20 units of U-75 insulin for a patient, but only U-50 and U-100 are available. How should the nurse mix the available insulin strengths?

A) 10 units of U-50 + 10 units of U-100
B) 12 units of U-50 + 8 units of U-100
C) 8 units of U-50 + 12 units of U-100
D) 15 units of U-50 + 5 units of U-100
E) 5 units of U-50 + 15 units of U-100

Answer: B) 12 units of U-50 + 8 units of U-100

Explanation:

• Use the proportional mix formula:
  • (75−50)×V₁₀₀ = (100−75)×V₅₀
  • 25×V₁₀₀ = 25×V₅₀
  • V₁₀₀ = V₅₀
• To get 20 units of U-75:
  • You need slightly more of the lower strength (U-50) to balance the higher strength (U-100).
  • Mixing 12 units of U-50 with 8 units of U-100 gives you the desired 20 units of U-75.

MCQ 6:

A patient is prescribed 15 units of U-65 insulin, but only U-30 and U-100 insulin are available. What should the pharmacist do to prepare the correct insulin dose?

A) 5 units of U-30 + 10 units of U-100
B) 10 units of U-30 + 5 units of U-100
C) 6 units of U-30 + 9 units of U-100
D) 9 units of U-30 + 6 units of U-100
E) 7 units of U-30 + 8 units of U-100

Answer: E) 7 units of U-30 + 8 units of U-100

Explanation:

• Use the proportional mix formula:
  • (65−30)×V₁₀₀ = (100−65)×V₃₀
  • 35×V₁₀₀ = 35×V₃₀
  • V₁₀₀ = V₃₀
• To prepare 15 units of U-65:
  • You need a balanced mix with slightly more of the higher concentration insulin.
  • Mixing 7 units of U-30 with 8 units of U-100 gives you the correct strength.

MCQ 7:

A healthcare provider needs to prepare 10 units of U-80 insulin, but only U-40 and U-100 insulin are available. How should the mix be prepared?

A) 3 units of U-40 + 7 units of U-100
B) 7 units of U-40 + 3 units of U-100
C) 4 units of U-40 + 6 units of U-100
D) 6 units of U-40 + 4 units of U-100
E) 5 units of U-40 + 5 units of U-100

Answer: A) 3 units of U-40 + 7 units of U-100

Explanation:

• Use the proportional mix formula:
  • (80−40)×V₁₀₀ = (100−80)×V₄₀
  • 40×V₁₀₀ = 20×V₄₀
  • 2×V₁₀₀ = V₄₀
• To get 10 units of U-80:
  • You need more of the higher concentration to achieve the desired mix.
  • Mixing 3 units of U-40 with 7 units of U-100 gives you the required 10 units of U-80.

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MCQ type: Dilution or Concentration

This method applies when you need to either dilute a higher strength insulin or concentrate a lower strength insulin to achieve the desired strength. This approach involves either adding a diluent to reduce the concentration or combining a lower concentration with a higher concentration to achieve the desired strength.

Scenario 1: Dilution of Insulin

If the available insulin strength is higher than the prescribed strength, you can dilute the insulin using a diluent to achieve the required concentration.

Example:

• Problem: Prescribed 10 units of U-50 insulin, but only U-100 insulin is available.
• Solution:
  • You need to dilute U-100 to U-50.
  • To do this, mix equal parts of U-100 insulin with an appropriate diluent (e.g., saline) to reduce the concentration by half.
  • Calculation:
    • 5 units of U-100 + 5 units of diluent = 10 units of U-50.
  • Explanation: By diluting U-100 insulin with an equal amount of diluent, you reduce the concentration to U-50, matching the prescribed dose.

Scenario 2: Concentrating Insulin

If the available insulin strength is lower than the prescribed strength, you can concentrate the insulin by combining it with a higher strength insulin.

Example:

• Problem: Prescribed 20 units of U-80 insulin, but only U-40 and U-100 are available.
• Solution:
  • You need to concentrate U-40 by combining it with U-100 to achieve the desired U-80 strength.
  • Calculation:
    • Using the same proportional mixing formula:
    • (80−40)×V₁₀₀ = (100−80)×V₄₀
    • 40×V₁₀₀ = 20×V₄₀
    • Assume V₁₀₀ = x and V₄₀ = 20−x.
    • Substitute and solve:
    • 40x = 20(20−x)
    • 40x = 400−20x
    • 60x = 400
    • x = 400/60 ≈ 6.67 units of U-100
    • V₄₀ = 20−6.67 = 13.33 units of U-40
  • Explanation: By mixing 6.67 units of U-100 with 13.33 units of U-40, you create 20 units of U-80 insulin.

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Insulin Dilution/Concentrating

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There are a few more types of insulin calculations, but they are more for MCQ1.

*** End of Chapter ***