Answer :
Let's calculate the required dosage for children weighing 10 pounds, 15 pounds, and 30 pounds, based on the provided guideline: 40 milligrams per 2.2 pounds of body weight, divided into three daily doses. We'll determine the number of teaspoons needed using the drug formula, which is 200 mg per 5 ml.
### Step-by-step Solution:
1. Determine the Total Daily Dosage:
- The recommended dosage is 40 mg for every 2.2 pounds of body weight.
2. Calculate for Each Child:
- For a 10-pound child:
- First, determine the total daily dosage in milligrams: [tex]\( \frac{10}{2.2} \times 40 \)[/tex].
- Calculate the amount of drug needed per single dose by dividing by 3 (because the total is divided into three doses per day).
- For a 15-pound child:
- Calculate the total daily dosage using: [tex]\( \frac{15}{2.2} \times 40 \)[/tex].
- Again, divide by 3 for the single dose amount.
- For a 30-pound child:
- Calculate the total daily dosage using: [tex]\( \frac{30}{2.2} \times 40 \)[/tex].
- Divide by 3 to find the amount needed per dose.
3. Convert the Dose from Milligrams to Teaspoons:
- The drug formula is 200 mg per 5 ml, and since 1 teaspoon is equivalent to 5 ml, each 5 ml is equivalent to 1 teaspoon.
- Convert the single dose from milligrams to milliliters (ml), then to teaspoons:
- Divide the single dose in mg by the concentration in mg/ml (which is [tex]\( \frac{200}{5} = 40 \)[/tex] mg/ml) to get the dose in ml.
- Convert the result from ml to teaspoons.
4. Round to the Nearest [tex]\( \frac{1}{4} \)[/tex] Teaspoon:
- Once you have the number of teaspoons, round the result to the nearest [tex]\( \frac{1}{4} \)[/tex] teaspoon.
### Results:
- For the 10-pound child, the rounded result is [tex]\( 3.25 \)[/tex] teaspoons.
- For the 15-pound child, the rounded result is [tex]\( 5.0 \)[/tex] teaspoons.
- For the 30-pound child, the rounded result is [tex]\( 10.0 \)[/tex] teaspoons.
These rounded amounts ensure each child receives the right dosage distributed across the day.
### Step-by-step Solution:
1. Determine the Total Daily Dosage:
- The recommended dosage is 40 mg for every 2.2 pounds of body weight.
2. Calculate for Each Child:
- For a 10-pound child:
- First, determine the total daily dosage in milligrams: [tex]\( \frac{10}{2.2} \times 40 \)[/tex].
- Calculate the amount of drug needed per single dose by dividing by 3 (because the total is divided into three doses per day).
- For a 15-pound child:
- Calculate the total daily dosage using: [tex]\( \frac{15}{2.2} \times 40 \)[/tex].
- Again, divide by 3 for the single dose amount.
- For a 30-pound child:
- Calculate the total daily dosage using: [tex]\( \frac{30}{2.2} \times 40 \)[/tex].
- Divide by 3 to find the amount needed per dose.
3. Convert the Dose from Milligrams to Teaspoons:
- The drug formula is 200 mg per 5 ml, and since 1 teaspoon is equivalent to 5 ml, each 5 ml is equivalent to 1 teaspoon.
- Convert the single dose from milligrams to milliliters (ml), then to teaspoons:
- Divide the single dose in mg by the concentration in mg/ml (which is [tex]\( \frac{200}{5} = 40 \)[/tex] mg/ml) to get the dose in ml.
- Convert the result from ml to teaspoons.
4. Round to the Nearest [tex]\( \frac{1}{4} \)[/tex] Teaspoon:
- Once you have the number of teaspoons, round the result to the nearest [tex]\( \frac{1}{4} \)[/tex] teaspoon.
### Results:
- For the 10-pound child, the rounded result is [tex]\( 3.25 \)[/tex] teaspoons.
- For the 15-pound child, the rounded result is [tex]\( 5.0 \)[/tex] teaspoons.
- For the 30-pound child, the rounded result is [tex]\( 10.0 \)[/tex] teaspoons.
These rounded amounts ensure each child receives the right dosage distributed across the day.
