Math Problem Statement

You receive a prescription for a baby containing the following dosing regimen of suspension A:

Take 6.5 mL twice a day for 14/7 then;

Take 3.5 mL twice a day for 10/7 then;

Take 1.5 mL three times a day for 7/7 then;

Take 1 mL once a day for 5/7

What volume (mL) of suspension A do you need to dispense for the full treatment course? Give your answer to 1 decimal place.

Solution

To calculate the total volume of suspension A required for the full treatment course, we need to sum the volumes used during each stage of the regimen.

  1. First stage: Take 6.5 mL twice a day for 14 days. Total for first stage=6.5mL×2times/day×14days=6.5×2×14=182mL\text{Total for first stage} = 6.5 \, \text{mL} \times 2 \, \text{times/day} \times 14 \, \text{days} = 6.5 \times 2 \times 14 = 182 \, \text{mL}

  2. Second stage: Take 3.5 mL twice a day for 10 days. Total for second stage=3.5mL×2times/day×10days=3.5×2×10=70mL\text{Total for second stage} = 3.5 \, \text{mL} \times 2 \, \text{times/day} \times 10 \, \text{days} = 3.5 \times 2 \times 10 = 70 \, \text{mL}

  3. Third stage: Take 1.5 mL three times a day for 7 days. Total for third stage=1.5mL×3times/day×7days=1.5×3×7=31.5mL\text{Total for third stage} = 1.5 \, \text{mL} \times 3 \, \text{times/day} \times 7 \, \text{days} = 1.5 \times 3 \times 7 = 31.5 \, \text{mL}

  4. Fourth stage: Take 1 mL once a day for 5 days. Total for fourth stage=1mL×1time/day×5days=1×1×5=5mL\text{Total for fourth stage} = 1 \, \text{mL} \times 1 \, \text{time/day} \times 5 \, \text{days} = 1 \times 1 \times 5 = 5 \, \text{mL}

Now, sum all the stages:

Total volume=182mL+70mL+31.5mL+5mL=288.5mL\text{Total volume} = 182 \, \text{mL} + 70 \, \text{mL} + 31.5 \, \text{mL} + 5 \, \text{mL} = 288.5 \, \text{mL}

So, the total volume of suspension A to be dispensed is 288.5 mL.

Would you like further details or clarification on any part of the calculation?

Here are 5 related questions to expand your understanding:

  1. What is the importance of calculating correct dosages for different age groups?
  2. How can errors in dosage calculations affect treatment outcomes?
  3. How would you handle a situation where the prescribed volume exceeds the available suspension size?
  4. What units are commonly used in dosage calculations besides milliliters?
  5. How do frequency and duration of a medication regimen impact total dosage volume?

Tip: When calculating dosages, always double-check the frequency (e.g., twice a day vs. once a day) to avoid medication errors.

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Math Problem Analysis

Mathematical Concepts

Arithmetic
Multiplication
Addition

Formulas

Total volume for each stage = Dose × Frequency × Duration
Total volume = Sum of volumes from all stages

Theorems

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Suitable Grade Level

Grades 5-7