Answer :
We start with the following information:
• The recommended dose is [tex]\(40\)[/tex] mg for every [tex]\(2.2\)[/tex] pounds of body weight per dose.
• The drug is provided as a liquid with a concentration of [tex]\(200\)[/tex] mg in [tex]\(5\)[/tex] mL, which simplifies to
[tex]\[
\frac{200 \text{ mg}}{5 \text{ mL}} = 40 \text{ mg/mL}.
\][/tex]
• One teaspoon is equal to [tex]\(5\)[/tex] mL.
• The dosage is divided into three daily doses (taken every [tex]\(8\)[/tex] hours).
We want to calculate the amount (in teaspoons) to be administered for a single dose for children weighing [tex]\(10\)[/tex], [tex]\(15\)[/tex], and [tex]\(30\)[/tex] pounds. The steps are as follows:
1. Calculate the Required Dose (mg) for Each Weight
For a child weighing [tex]\(w\)[/tex] pounds, the dose in milligrams per dose is given by:
[tex]\[
\text{Dose (mg)} = 40 \times \left(\frac{w}{2.2}\right).
\][/tex]
For each weight:
- For [tex]\(10\)[/tex] lbs:
[tex]\[
40 \times \left(\frac{10}{2.2}\right) \approx 181.82 \text{ mg},
\][/tex]
- For [tex]\(15\)[/tex] lbs:
[tex]\[
40 \times \left(\frac{15}{2.2}\right) \approx 272.73 \text{ mg},
\][/tex]
- For [tex]\(30\)[/tex] lbs:
[tex]\[
40 \times \left(\frac{30}{2.2}\right) \approx 545.45 \text{ mg}.
\][/tex]
2. Convert the Dose from mg to mL
Since the liquid has [tex]\(40\)[/tex] mg per mL, the volume (in mL) required is:
[tex]\[
\text{Volume (mL)} = \frac{\text{Dose (mg)}}{40}.
\][/tex]
For each weight:
- For [tex]\(10\)[/tex] lbs:
[tex]\[
\frac{181.82}{40} \approx 4.545 \text{ mL},
\][/tex]
- For [tex]\(15\)[/tex] lbs:
[tex]\[
\frac{272.73}{40} \approx 6.818 \text{ mL},
\][/tex]
- For [tex]\(30\)[/tex] lbs:
[tex]\[
\frac{545.45}{40} \approx 13.636 \text{ mL}.
\][/tex]
3. Convert the Volume from mL to Teaspoons
Since [tex]\(1\)[/tex] teaspoon is [tex]\(5\)[/tex] mL, the number of teaspoons is:
[tex]\[
\text{Teaspoons} = \frac{\text{Volume (mL)}}{5}.
\][/tex]
For each weight:
- For [tex]\(10\)[/tex] lbs:
[tex]\[
\frac{4.545}{5} \approx 0.909 \text{ tsp},
\][/tex]
- For [tex]\(15\)[/tex] lbs:
[tex]\[
\frac{6.818}{5} \approx 1.364 \text{ tsp},
\][/tex]
- For [tex]\(30\)[/tex] lbs:
[tex]\[
\frac{13.636}{5} \approx 2.727 \text{ tsp}.
\][/tex]
4. Round Each Result Up to the Nearest [tex]$\frac{1}{4}$[/tex] Teaspoon
To round up to the nearest [tex]\(\frac{1}{4}\)[/tex] teaspoon, we adjust the numbers as follows:
- For [tex]\(0.909\)[/tex] tsp, rounding up gives [tex]\(1.0\)[/tex] tsp.
- For [tex]\(1.364\)[/tex] tsp, rounding up gives [tex]\(1.5\)[/tex] tsp.
- For [tex]\(2.727\)[/tex] tsp, rounding up gives [tex]\(2.75\)[/tex] tsp.
Thus, the number of teaspoons required for each entry is:
- [tex]\(10\)[/tex] lbs: [tex]\(1\)[/tex] teaspoon,
- [tex]\(15\)[/tex] lbs: [tex]\(1 \frac{1}{2}\)[/tex] teaspoons,
- [tex]\(30\)[/tex] lbs: [tex]\(2 \frac{3}{4}\)[/tex] teaspoons.
Therefore, the correct answer is:
[tex]$$\boxed{1,\quad 1\frac{1}{2},\quad 2\frac{3}{4}}$$[/tex]
• The recommended dose is [tex]\(40\)[/tex] mg for every [tex]\(2.2\)[/tex] pounds of body weight per dose.
• The drug is provided as a liquid with a concentration of [tex]\(200\)[/tex] mg in [tex]\(5\)[/tex] mL, which simplifies to
[tex]\[
\frac{200 \text{ mg}}{5 \text{ mL}} = 40 \text{ mg/mL}.
\][/tex]
• One teaspoon is equal to [tex]\(5\)[/tex] mL.
• The dosage is divided into three daily doses (taken every [tex]\(8\)[/tex] hours).
We want to calculate the amount (in teaspoons) to be administered for a single dose for children weighing [tex]\(10\)[/tex], [tex]\(15\)[/tex], and [tex]\(30\)[/tex] pounds. The steps are as follows:
1. Calculate the Required Dose (mg) for Each Weight
For a child weighing [tex]\(w\)[/tex] pounds, the dose in milligrams per dose is given by:
[tex]\[
\text{Dose (mg)} = 40 \times \left(\frac{w}{2.2}\right).
\][/tex]
For each weight:
- For [tex]\(10\)[/tex] lbs:
[tex]\[
40 \times \left(\frac{10}{2.2}\right) \approx 181.82 \text{ mg},
\][/tex]
- For [tex]\(15\)[/tex] lbs:
[tex]\[
40 \times \left(\frac{15}{2.2}\right) \approx 272.73 \text{ mg},
\][/tex]
- For [tex]\(30\)[/tex] lbs:
[tex]\[
40 \times \left(\frac{30}{2.2}\right) \approx 545.45 \text{ mg}.
\][/tex]
2. Convert the Dose from mg to mL
Since the liquid has [tex]\(40\)[/tex] mg per mL, the volume (in mL) required is:
[tex]\[
\text{Volume (mL)} = \frac{\text{Dose (mg)}}{40}.
\][/tex]
For each weight:
- For [tex]\(10\)[/tex] lbs:
[tex]\[
\frac{181.82}{40} \approx 4.545 \text{ mL},
\][/tex]
- For [tex]\(15\)[/tex] lbs:
[tex]\[
\frac{272.73}{40} \approx 6.818 \text{ mL},
\][/tex]
- For [tex]\(30\)[/tex] lbs:
[tex]\[
\frac{545.45}{40} \approx 13.636 \text{ mL}.
\][/tex]
3. Convert the Volume from mL to Teaspoons
Since [tex]\(1\)[/tex] teaspoon is [tex]\(5\)[/tex] mL, the number of teaspoons is:
[tex]\[
\text{Teaspoons} = \frac{\text{Volume (mL)}}{5}.
\][/tex]
For each weight:
- For [tex]\(10\)[/tex] lbs:
[tex]\[
\frac{4.545}{5} \approx 0.909 \text{ tsp},
\][/tex]
- For [tex]\(15\)[/tex] lbs:
[tex]\[
\frac{6.818}{5} \approx 1.364 \text{ tsp},
\][/tex]
- For [tex]\(30\)[/tex] lbs:
[tex]\[
\frac{13.636}{5} \approx 2.727 \text{ tsp}.
\][/tex]
4. Round Each Result Up to the Nearest [tex]$\frac{1}{4}$[/tex] Teaspoon
To round up to the nearest [tex]\(\frac{1}{4}\)[/tex] teaspoon, we adjust the numbers as follows:
- For [tex]\(0.909\)[/tex] tsp, rounding up gives [tex]\(1.0\)[/tex] tsp.
- For [tex]\(1.364\)[/tex] tsp, rounding up gives [tex]\(1.5\)[/tex] tsp.
- For [tex]\(2.727\)[/tex] tsp, rounding up gives [tex]\(2.75\)[/tex] tsp.
Thus, the number of teaspoons required for each entry is:
- [tex]\(10\)[/tex] lbs: [tex]\(1\)[/tex] teaspoon,
- [tex]\(15\)[/tex] lbs: [tex]\(1 \frac{1}{2}\)[/tex] teaspoons,
- [tex]\(30\)[/tex] lbs: [tex]\(2 \frac{3}{4}\)[/tex] teaspoons.
Therefore, the correct answer is:
[tex]$$\boxed{1,\quad 1\frac{1}{2},\quad 2\frac{3}{4}}$$[/tex]
