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A 10 kg child requires a dose of 60 mg/kg/day of a medication, administered twice daily. The available suspension is 250 mg/5 mL. Calculate the dose per administration and the total volume of suspensi

Mathematics

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Answers

3 parts
a

300 mg\text{300 mg}

b

84 mL\text{84 mL}

c

8.4 tablets\text{8.4 tablets}

Step-by-step solution

7 steps

Here's the solution to the problem:

Given Information:

  • Patient weight: 10 kg10 \text{ kg}
  • Dose: 60 mg/kg/day60 \text{ mg/kg/day}
  • Frequency: Twice daily (BID)
  • Duration: 7 days7 \text{ days}
  • Suspension strength: 250 mg/5 mL250 \text{ mg/5 mL}
  • Tablet strength: 500 mg/tablet500 \text{ mg/tablet}

Part a· 2 steps

What is the required dose per administration?

  1. Calculate the total daily dose.

    Total daily dose=Dose per kg per day×Patient weight\text{Total daily dose} = \text{Dose per kg per day} \times \text{Patient weight} Total daily dose=60 mg/kg/day×10 kg=600 mg/day\text{Total daily dose} = 60 \text{ mg/kg/day} \times 10 \text{ kg} = 600 \text{ mg/day}
  2. Calculate the dose per administration.

    Since the medication is taken twice daily (BID), there are 2 administrations per day.

    Dose per administration=Total daily doseNumber of administrations per day\text{Dose per administration} = \frac{\text{Total daily dose}}{\text{Number of administrations per day}} Dose per administration=600 mg/day2 administrations/day=300 mg/administration\text{Dose per administration} = \frac{600 \text{ mg/day}}{2 \text{ administrations/day}} = 300 \text{ mg/administration}

    The required dose per administration is 300 mg\boxed{\text{300 mg}}.


Part b

84 mL\text{84 mL}

What is the total volume of suspension required?

  1. Calculate the total amount of drug needed for the entire 7-day course.

    Total drug needed=Total daily dose×Duration\text{Total drug needed} = \text{Total daily dose} \times \text{Duration} Total drug needed=600 mg/day×7 days=4200 mg\text{Total drug needed} = 600 \text{ mg/day} \times 7 \text{ days} = 4200 \text{ mg}
  2. Determine the concentration of the suspension in mg/mL.

    Suspension concentration=250 mg5 mL=50 mg/mL\text{Suspension concentration} = \frac{250 \text{ mg}}{5 \text{ mL}} = 50 \text{ mg/mL}
  3. Calculate the total volume of suspension required.

    Total volume of suspension=Total drug neededSuspension concentration\text{Total volume of suspension} = \frac{\text{Total drug needed}}{\text{Suspension concentration}} Total volume of suspension=4200 mg50 mg/mL=84 mL\text{Total volume of suspension} = \frac{4200 \text{ mg}}{50 \text{ mg/mL}} = 84 \text{ mL}

    The total volume of suspension required is 84 mL\boxed{\text{84 mL}}.


Part c

8.4 tablets\text{8.4 tablets}

How many 500 mg tablets are needed to compound the suspension?

  1. Use the total amount of drug needed for the entire course, calculated in part b.

    Total drug needed=4200 mg\text{Total drug needed} = 4200 \text{ mg}
  2. Calculate the number of tablets required based on the tablet strength.

    Number of tablets=Total drug neededTablet strength\text{Number of tablets} = \frac{\text{Total drug needed}}{\text{Tablet strength}} Number of tablets=4200 mg500 mg/tablet=8.4 tablets\text{Number of tablets} = \frac{4200 \text{ mg}}{500 \text{ mg/tablet}} = 8.4 \text{ tablets}

    The number of 500 mg tablets needed to compound the suspension is 8.4 tablets\boxed{\text{8.4 tablets}}.

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