Dimensional Analysis - Complex

1. Units and Conversion 1.6) Dimensional Analysis 1.6.1) Dimensional Analysis

1.6.1.1) Dimensional Analysis Hard 1


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A 254 lb patient is taking a chemo drug costing 38.14 cent per mg. The recommended dose is 13.3 mg per kg of body weight. The nurse is administering a solution of 2.66 mg/mL concentration and the pump is infusing it at the rate of 1.7 mL/min. The tubing of this particular pump delivers 18 gtt/mL.

Calculate the total cost of the drug used for this patient, in USD.


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lb equals 585.66 kg

    • This problem has the following paired information:
      38.14 cent = 1 mg drug
      2.66 mg drug = 1 mL solution
      13.3 mg drug = 1 kg body weight
      1.7 ml solution = 1 min
      18 drops = 1 mL solution
      patient's body weight = 254 lb
      Also, you need to know that 1 kg = 2.2 lb.

    Since this problem is asking cost, we take the relationship which has cent in it, and keep at the first denominator
    38.14 cent × 13.3 mg × 1 kg × 254 lb
    1 mg 1 kg 2.2 lb 1

    Therefore, the cost in cent is = 58565.7.
    Therefore, the cost in USD is =585.66. Ans.


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