Answer :
To solve the problem of determining the amount of drug (in teaspoons) needed for children weighing 10 pounds, 15 pounds, and 20 pounds, follow these steps:
1. Understand the Dosage Requirement:
- The recommended dosage is typically 10 mg per kilogram of body weight per day, divided into three doses.
2. Convert Pounds to Kilograms:
- Since 1 kilogram equals approximately 2.20462 pounds, you must convert the children's weights from pounds to kilograms.
- For a child weighing 10 lbs:
[tex]\[ \text{Weight in kg} = \frac{10}{2.20462} \approx 4.54 \text{ kg} \][/tex]
- For a child weighing 15 lbs:
[tex]\[ \text{Weight in kg} = \frac{15}{2.20462} \approx 6.80 \text{ kg} \][/tex]
- For a child weighing 20 lbs:
[tex]\[ \text{Weight in kg} = \frac{20}{2.20462} \approx 9.07 \text{ kg} \][/tex]
3. Calculate Total Daily Dosage in mg:
- For each child's weight, multiply by the dosage recommendation of 10 mg per kg.
- For 10 lbs (4.54 kg):
[tex]\[ \text{Total mg per day} = 4.54 \times 10 = 45.4 \, \text{mg} \][/tex]
- For 15 lbs (6.80 kg):
[tex]\[ \text{Total mg per day} = 6.80 \times 10 = 68.0 \, \text{mg} \][/tex]
- For 20 lbs (9.07 kg):
[tex]\[ \text{Total mg per day} = 9.07 \times 10 = 90.7 \, \text{mg} \][/tex]
4. Convert the Dosage to Milliliters:
- Knowing that 200 mg is contained in 5 ml, we find out how many ml are needed for the total daily dose.
- For 10 lbs:
[tex]\[ \text{Total ml per day} = \frac{45.4}{200} \times 5 = 1.135 \text{ ml} \][/tex]
- For 15 lbs:
[tex]\[ \text{Total ml per day} = \frac{68.0}{200} \times 5 = 1.7 \text{ ml} \][/tex]
- For 20 lbs:
[tex]\[ \text{Total ml per day} = \frac{90.7}{200} \times 5 = 2.2675 \text{ ml} \][/tex]
5. Convert Milliliters to Teaspoons:
- Since 1 teaspoon equals 5 ml, divide by 5 to convert ml to teaspoons.
- For 10 lbs:
[tex]\[ \text{Total teaspoons} = \frac{1.135}{5} \approx 0.23 \text{ teaspoon} \][/tex]
- For 15 lbs:
[tex]\[ \text{Total teaspoons} = \frac{1.7}{5} \approx 0.34 \text{ teaspoon} \][/tex]
- For 20 lbs:
[tex]\[ \text{Total teaspoons} = \frac{2.2675}{5} \approx 0.45 \text{ teaspoon} \][/tex]
Thus, the amounts required are approximately 0.23 teaspoons for 10 pounds, 0.34 teaspoons for 15 pounds, and 0.45 teaspoons for 20 pounds.
1. Understand the Dosage Requirement:
- The recommended dosage is typically 10 mg per kilogram of body weight per day, divided into three doses.
2. Convert Pounds to Kilograms:
- Since 1 kilogram equals approximately 2.20462 pounds, you must convert the children's weights from pounds to kilograms.
- For a child weighing 10 lbs:
[tex]\[ \text{Weight in kg} = \frac{10}{2.20462} \approx 4.54 \text{ kg} \][/tex]
- For a child weighing 15 lbs:
[tex]\[ \text{Weight in kg} = \frac{15}{2.20462} \approx 6.80 \text{ kg} \][/tex]
- For a child weighing 20 lbs:
[tex]\[ \text{Weight in kg} = \frac{20}{2.20462} \approx 9.07 \text{ kg} \][/tex]
3. Calculate Total Daily Dosage in mg:
- For each child's weight, multiply by the dosage recommendation of 10 mg per kg.
- For 10 lbs (4.54 kg):
[tex]\[ \text{Total mg per day} = 4.54 \times 10 = 45.4 \, \text{mg} \][/tex]
- For 15 lbs (6.80 kg):
[tex]\[ \text{Total mg per day} = 6.80 \times 10 = 68.0 \, \text{mg} \][/tex]
- For 20 lbs (9.07 kg):
[tex]\[ \text{Total mg per day} = 9.07 \times 10 = 90.7 \, \text{mg} \][/tex]
4. Convert the Dosage to Milliliters:
- Knowing that 200 mg is contained in 5 ml, we find out how many ml are needed for the total daily dose.
- For 10 lbs:
[tex]\[ \text{Total ml per day} = \frac{45.4}{200} \times 5 = 1.135 \text{ ml} \][/tex]
- For 15 lbs:
[tex]\[ \text{Total ml per day} = \frac{68.0}{200} \times 5 = 1.7 \text{ ml} \][/tex]
- For 20 lbs:
[tex]\[ \text{Total ml per day} = \frac{90.7}{200} \times 5 = 2.2675 \text{ ml} \][/tex]
5. Convert Milliliters to Teaspoons:
- Since 1 teaspoon equals 5 ml, divide by 5 to convert ml to teaspoons.
- For 10 lbs:
[tex]\[ \text{Total teaspoons} = \frac{1.135}{5} \approx 0.23 \text{ teaspoon} \][/tex]
- For 15 lbs:
[tex]\[ \text{Total teaspoons} = \frac{1.7}{5} \approx 0.34 \text{ teaspoon} \][/tex]
- For 20 lbs:
[tex]\[ \text{Total teaspoons} = \frac{2.2675}{5} \approx 0.45 \text{ teaspoon} \][/tex]
Thus, the amounts required are approximately 0.23 teaspoons for 10 pounds, 0.34 teaspoons for 15 pounds, and 0.45 teaspoons for 20 pounds.
