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Answer :
We start by computing the dosage per administration. The recommended dose is
[tex]$$
40\,\text{mg per }2.2\,\text{lb}
$$[/tex]
so for a child weighing [tex]$W$[/tex] pounds the dose in milligrams is
[tex]$$
\text{Dose}_{\text{mg}} = 40 \left(\frac{W}{2.2}\right).
$$[/tex]
Next, notice that the drug is supplied as
[tex]$$
200\,\text{mg in }5\,\text{ml}.
$$[/tex]
This means the concentration is
[tex]$$
\frac{200\, \text{mg}}{5\, \text{ml}} = 40\,\text{mg/ml}.
$$[/tex]
Thus, the volume in milliliters needed for one dose is
[tex]$$
\text{Volume}_{\text{ml}} = \frac{\text{Dose}_{\text{mg}}}{40}.
$$[/tex]
Since one teaspoon equals 5 ml, the number of teaspoons per dose is given by
[tex]$$
\text{Teaspoons} = \frac{\text{Volume}_{\text{ml}}}{5}.
$$[/tex]
We now perform these calculations for each weight.
---
For a child weighing 10 lb:
1. Calculate the dose in mg:
[tex]$$
\text{Dose}_{\text{mg}} = 40 \left(\frac{10}{2.2}\right) \approx 40 \times 4.5455 \approx 181.82\,\text{mg}.
$$[/tex]
2. Compute the volume in ml:
[tex]$$
\text{Volume}_{\text{ml}} = \frac{181.82}{40} \approx 4.5455\,\text{ml}.
$$[/tex]
3. Convert to teaspoons:
[tex]$$
\text{Teaspoons} = \frac{4.5455}{5} \approx 0.9091.
$$[/tex]
4. Rounding [tex]$0.9091$[/tex] to the nearest [tex]$\frac{1}{4}$[/tex] teaspoon gives approximately [tex]$1.0$[/tex] teaspoon.
---
For a child weighing 15 lb:
1. Calculate the dose in mg:
[tex]$$
\text{Dose}_{\text{mg}} = 40 \left(\frac{15}{2.2}\right) \approx 40 \times 6.8182 \approx 272.73\,\text{mg}.
$$[/tex]
2. Compute the volume in ml:
[tex]$$
\text{Volume}_{\text{ml}} = \frac{272.73}{40} \approx 6.8182\,\text{ml}.
$$[/tex]
3. Convert to teaspoons:
[tex]$$
\text{Teaspoons} = \frac{6.8182}{5} \approx 1.3636.
$$[/tex]
4. Rounding [tex]$1.3636$[/tex] to the nearest [tex]$\frac{1}{4}$[/tex] teaspoon gives approximately [tex]$1.5$[/tex] teaspoons.
---
For a child weighing 30 lb:
1. Calculate the dose in mg:
[tex]$$
\text{Dose}_{\text{mg}} = 40 \left(\frac{30}{2.2}\right) \approx 40 \times 13.6364 \approx 545.45\,\text{mg}.
$$[/tex]
2. Compute the volume in ml:
[tex]$$
\text{Volume}_{\text{ml}} = \frac{545.45}{40} \approx 13.6364\,\text{ml}.
$$[/tex]
3. Convert to teaspoons:
[tex]$$
\text{Teaspoons} = \frac{13.6364}{5} \approx 2.7273.
$$[/tex]
4. Rounding [tex]$2.7273$[/tex] to the nearest [tex]$\frac{1}{4}$[/tex] teaspoon gives approximately [tex]$2.75$[/tex] teaspoons.
---
Thus, the number of teaspoons required for children weighing 10 lb, 15 lb, and 30 lb per dose are approximately
[tex]$$
1,\quad 1\frac{1}{2},\quad 2\frac{3}{4},
$$[/tex]
which corresponds to answer choice A.
[tex]$$
40\,\text{mg per }2.2\,\text{lb}
$$[/tex]
so for a child weighing [tex]$W$[/tex] pounds the dose in milligrams is
[tex]$$
\text{Dose}_{\text{mg}} = 40 \left(\frac{W}{2.2}\right).
$$[/tex]
Next, notice that the drug is supplied as
[tex]$$
200\,\text{mg in }5\,\text{ml}.
$$[/tex]
This means the concentration is
[tex]$$
\frac{200\, \text{mg}}{5\, \text{ml}} = 40\,\text{mg/ml}.
$$[/tex]
Thus, the volume in milliliters needed for one dose is
[tex]$$
\text{Volume}_{\text{ml}} = \frac{\text{Dose}_{\text{mg}}}{40}.
$$[/tex]
Since one teaspoon equals 5 ml, the number of teaspoons per dose is given by
[tex]$$
\text{Teaspoons} = \frac{\text{Volume}_{\text{ml}}}{5}.
$$[/tex]
We now perform these calculations for each weight.
---
For a child weighing 10 lb:
1. Calculate the dose in mg:
[tex]$$
\text{Dose}_{\text{mg}} = 40 \left(\frac{10}{2.2}\right) \approx 40 \times 4.5455 \approx 181.82\,\text{mg}.
$$[/tex]
2. Compute the volume in ml:
[tex]$$
\text{Volume}_{\text{ml}} = \frac{181.82}{40} \approx 4.5455\,\text{ml}.
$$[/tex]
3. Convert to teaspoons:
[tex]$$
\text{Teaspoons} = \frac{4.5455}{5} \approx 0.9091.
$$[/tex]
4. Rounding [tex]$0.9091$[/tex] to the nearest [tex]$\frac{1}{4}$[/tex] teaspoon gives approximately [tex]$1.0$[/tex] teaspoon.
---
For a child weighing 15 lb:
1. Calculate the dose in mg:
[tex]$$
\text{Dose}_{\text{mg}} = 40 \left(\frac{15}{2.2}\right) \approx 40 \times 6.8182 \approx 272.73\,\text{mg}.
$$[/tex]
2. Compute the volume in ml:
[tex]$$
\text{Volume}_{\text{ml}} = \frac{272.73}{40} \approx 6.8182\,\text{ml}.
$$[/tex]
3. Convert to teaspoons:
[tex]$$
\text{Teaspoons} = \frac{6.8182}{5} \approx 1.3636.
$$[/tex]
4. Rounding [tex]$1.3636$[/tex] to the nearest [tex]$\frac{1}{4}$[/tex] teaspoon gives approximately [tex]$1.5$[/tex] teaspoons.
---
For a child weighing 30 lb:
1. Calculate the dose in mg:
[tex]$$
\text{Dose}_{\text{mg}} = 40 \left(\frac{30}{2.2}\right) \approx 40 \times 13.6364 \approx 545.45\,\text{mg}.
$$[/tex]
2. Compute the volume in ml:
[tex]$$
\text{Volume}_{\text{ml}} = \frac{545.45}{40} \approx 13.6364\,\text{ml}.
$$[/tex]
3. Convert to teaspoons:
[tex]$$
\text{Teaspoons} = \frac{13.6364}{5} \approx 2.7273.
$$[/tex]
4. Rounding [tex]$2.7273$[/tex] to the nearest [tex]$\frac{1}{4}$[/tex] teaspoon gives approximately [tex]$2.75$[/tex] teaspoons.
---
Thus, the number of teaspoons required for children weighing 10 lb, 15 lb, and 30 lb per dose are approximately
[tex]$$
1,\quad 1\frac{1}{2},\quad 2\frac{3}{4},
$$[/tex]
which corresponds to answer choice A.
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