What dosage in grams per kilogram of body weight does a 128 lb woman receive if she takes two 225 mg tablets of penicillin

What dosage in grams per kilogram of body weight does a 128 lb woman receive if she takes two 225 mg tablets of penicillin? Express your answer using two significant figures. How many 125 mg tablets should a 30 lb child take in the same dosage? Express your answer using two significant figures.

The Correct Answer and Explanation is:

Part A: Dosage for a 128 lb woman taking two 225 mg tablets

1. Total dosage taken: 2 tablets × 225 mg = 450 mg
2. Convert milligrams to grams: 450 mg ÷ 1000 = 0.450 g
3. Convert pounds to kilograms: 128 lb ÷ 2.20462 ≈ 58.06 kg
4. Dosage in grams per kilogram: 0.450 g ÷ 58.06 kg ≈ 0.00775 g/kg
5. Rounded to two significant figures: 0.0078 g/kg

Part B: Number of 125 mg tablets for a 30 lb child at the same dosage

1. Convert pounds to kilograms: 30 lb ÷ 2.20462 ≈ 13.61 kg
2. Required dosage in grams: 0.0078 g/kg × 13.61 kg ≈ 0.106 g
3. Convert grams to milligrams: 0.106 g × 1000 = 106 mg
4. Number of tablets needed: 106 mg ÷ 125 mg/tablet ≈ 0.848 tablets
5. Rounded to two significant figures: 0.85 tablets

Explanation

This problem is a classic example of medical dosage calculation, where consistency of units and precision of significant figures are crucial. In Part A, the goal is to determine how much medication in grams per kilogram a 128 lb woman receives when she takes two tablets of 225 mg penicillin. The first step is to find the total dose taken, which is straightforward multiplication. Since dosage per body weight is commonly expressed in grams per kilogram, converting from milligrams to grams and from pounds to kilograms is essential.

Once the total dose in grams and the body weight in kilograms are known, dividing the two gives the required ratio. Rounding the result to two significant figures ensures appropriate scientific communication and reflects the precision of the original data.

In Part B, this calculated dosage per kilogram is applied to a child weighing 30 lb. The same conversions are repeated in reverse to determine how much total medication the child would need for an equivalent dose per body weight. After converting to milligrams, the dosage is compared to the available 125 mg tablet size to determine how many tablets would be needed. The result is slightly less than one full tablet, which is common in pediatric dosing and may require adjustment or splitting.

This approach ensures patients of different sizes receive appropriately scaled doses, promoting both effectiveness and safety in medical treatments.