Answer :
To determine the number of teaspoons required for each weight category, let's break it down into simple steps:
1. Understand the Dosage Requirement:
- The recommended dosage is 40 milligrams (mg) of the medication for every 2.2 pounds of body weight. This dosage should be split into three doses throughout the day.
2. Drug Formula:
- The drug is supplied as 200 milligrams in 5 milliliters (ml), which is equivalent to 1 teaspoon (tsp) because 1 teaspoon equals 5 ml.
3. Calculate the Dosage for Each Weight:
For simplicity, let's calculate for each given weight category:
- 10 pounds:
- Calculate the total daily dosage in milligrams:
[tex]\[
\frac{40 \text{ mg}}{2.2 \text{ pounds}} \times 10 \text{ pounds} = 181.82 \text{ mg}
\][/tex]
- Divide by three to get the dosage per dose:
[tex]\[
\frac{181.82 \text{ mg}}{3} \approx 60.61 \text{ mg per dose}
\][/tex]
- Convert to ml using the concentration (200 mg in 5 ml):
[tex]\[
\frac{60.61 \text{ mg}}{\frac{200 \text{ mg}}{5 \text{ ml}}} \approx 1.515 \text{ ml}
\][/tex]
- Convert ml to teaspoons (5 ml = 1 tsp):
[tex]\[
\frac{1.515 \text{ ml}}{5 \text{ ml/tsp}} \approx 0.303 \text{ tsp}
\][/tex]
- Round to the nearest 1/4 teaspoon:
[tex]\[
\approx 0.25 \text{ tsp}
\][/tex]
- 15 pounds:
- Calculate the total daily dosage in milligrams:
[tex]\[
\frac{40 \text{ mg}}{2.2 \text{ pounds}} \times 15 \text{ pounds} = 272.73 \text{ mg}
\][/tex]
- Divide by three to get the dosage per dose:
[tex]\[
\frac{272.73 \text{ mg}}{3} \approx 90.91 \text{ mg per dose}
\][/tex]
- Convert to ml using the concentration:
[tex]\[
\frac{90.91 \text{ mg}}{\frac{200 \text{ mg}}{5 \text{ ml}}} \approx 2.273 \text{ ml}
\][/tex]
- Convert ml to teaspoons:
[tex]\[
\frac{2.273 \text{ ml}}{5 \text{ ml/tsp}} \approx 0.455 \text{ tsp}
\][/tex]
- Round to the nearest 1/4 teaspoon:
[tex]\[
\approx 0.5 \text{ tsp}
\][/tex]
- 30 pounds:
- Calculate the total daily dosage in milligrams:
[tex]\[
\frac{40 \text{ mg}}{2.2 \text{ pounds}} \times 30 \text{ pounds} = 545.45 \text{ mg}
\][/tex]
- Divide by three to get the dosage per dose:
[tex]\[
\frac{545.45 \text{ mg}}{3} \approx 181.82 \text{ mg per dose}
\][/tex]
- Convert to ml using the concentration:
[tex]\[
\frac{181.82 \text{ mg}}{\frac{200 \text{ mg}}{5 \text{ ml}}} \approx 4.545 \text{ ml}
\][/tex]
- Convert ml to teaspoons:
[tex]\[
\frac{4.545 \text{ ml}}{5 \text{ ml/tsp}} \approx 0.909 \text{ tsp}
\][/tex]
- Round to the nearest 1/4 teaspoon:
[tex]\[
\approx 1.0 \text{ tsp}
\][/tex]
By following these steps, we find that the required teaspoons for each weight are approximately 0.25 tsp for 10 pounds, 0.5 tsp for 15 pounds, and 1.0 tsp for 30 pounds.
1. Understand the Dosage Requirement:
- The recommended dosage is 40 milligrams (mg) of the medication for every 2.2 pounds of body weight. This dosage should be split into three doses throughout the day.
2. Drug Formula:
- The drug is supplied as 200 milligrams in 5 milliliters (ml), which is equivalent to 1 teaspoon (tsp) because 1 teaspoon equals 5 ml.
3. Calculate the Dosage for Each Weight:
For simplicity, let's calculate for each given weight category:
- 10 pounds:
- Calculate the total daily dosage in milligrams:
[tex]\[
\frac{40 \text{ mg}}{2.2 \text{ pounds}} \times 10 \text{ pounds} = 181.82 \text{ mg}
\][/tex]
- Divide by three to get the dosage per dose:
[tex]\[
\frac{181.82 \text{ mg}}{3} \approx 60.61 \text{ mg per dose}
\][/tex]
- Convert to ml using the concentration (200 mg in 5 ml):
[tex]\[
\frac{60.61 \text{ mg}}{\frac{200 \text{ mg}}{5 \text{ ml}}} \approx 1.515 \text{ ml}
\][/tex]
- Convert ml to teaspoons (5 ml = 1 tsp):
[tex]\[
\frac{1.515 \text{ ml}}{5 \text{ ml/tsp}} \approx 0.303 \text{ tsp}
\][/tex]
- Round to the nearest 1/4 teaspoon:
[tex]\[
\approx 0.25 \text{ tsp}
\][/tex]
- 15 pounds:
- Calculate the total daily dosage in milligrams:
[tex]\[
\frac{40 \text{ mg}}{2.2 \text{ pounds}} \times 15 \text{ pounds} = 272.73 \text{ mg}
\][/tex]
- Divide by three to get the dosage per dose:
[tex]\[
\frac{272.73 \text{ mg}}{3} \approx 90.91 \text{ mg per dose}
\][/tex]
- Convert to ml using the concentration:
[tex]\[
\frac{90.91 \text{ mg}}{\frac{200 \text{ mg}}{5 \text{ ml}}} \approx 2.273 \text{ ml}
\][/tex]
- Convert ml to teaspoons:
[tex]\[
\frac{2.273 \text{ ml}}{5 \text{ ml/tsp}} \approx 0.455 \text{ tsp}
\][/tex]
- Round to the nearest 1/4 teaspoon:
[tex]\[
\approx 0.5 \text{ tsp}
\][/tex]
- 30 pounds:
- Calculate the total daily dosage in milligrams:
[tex]\[
\frac{40 \text{ mg}}{2.2 \text{ pounds}} \times 30 \text{ pounds} = 545.45 \text{ mg}
\][/tex]
- Divide by three to get the dosage per dose:
[tex]\[
\frac{545.45 \text{ mg}}{3} \approx 181.82 \text{ mg per dose}
\][/tex]
- Convert to ml using the concentration:
[tex]\[
\frac{181.82 \text{ mg}}{\frac{200 \text{ mg}}{5 \text{ ml}}} \approx 4.545 \text{ ml}
\][/tex]
- Convert ml to teaspoons:
[tex]\[
\frac{4.545 \text{ ml}}{5 \text{ ml/tsp}} \approx 0.909 \text{ tsp}
\][/tex]
- Round to the nearest 1/4 teaspoon:
[tex]\[
\approx 1.0 \text{ tsp}
\][/tex]
By following these steps, we find that the required teaspoons for each weight are approximately 0.25 tsp for 10 pounds, 0.5 tsp for 15 pounds, and 1.0 tsp for 30 pounds.
