Answer :
We begin by calculating the dosage (in milligrams) per dose for a child of weight [tex]$w$[/tex] pounds. The recommendation is to give 40 mg per 2.2 pounds. Thus, the milligram dose is
[tex]$$
\text{dose}_{\text{mg}} = \frac{w}{2.2} \times 40.
$$[/tex]
Since the drug comes in a formulation of 200 mg in 5 mL, its concentration is
[tex]$$
\frac{200 \text{ mg}}{5 \text{ mL}} = 40 \text{ mg/mL}.
$$[/tex]
To convert the milligram dose to a volume in milliliters, we use
[tex]$$
\text{dose}_{\text{mL}} = \frac{\text{dose}_{\text{mg}}}{40}.
$$[/tex]
Knowing that 1 teaspoon equals 5 mL, the corresponding dose in teaspoons is
[tex]$$
\text{dose}_{\text{tsp}} = \frac{\text{dose}_{\text{mL}}}{5} = \frac{\text{dose}_{\text{mg}}}{200}.
$$[/tex]
Substitute the expression for [tex]$\text{dose}_{\text{mg}}$[/tex]:
[tex]$$
\text{dose}_{\text{tsp}} = \frac{\frac{w}{2.2} \times 40}{200} = \frac{w}{2.2} \times \frac{40}{200} = \frac{w}{2.2} \times 0.2.
$$[/tex]
Now, we calculate the dosage for each given weight and then round upward to the nearest [tex]$\frac{1}{4}$[/tex] teaspoon.
1. For [tex]$w = 10$[/tex] pounds:
[tex]$$
\text{dose}_{\text{tsp}} = \frac{10}{2.2} \times 0.2 \approx 0.9091 \text{ teaspoons}.
$$[/tex]
Rounding upward to the nearest quarter teaspoon, we get:
[tex]$$
1.00 \text{ teaspoon}.
$$[/tex]
2. For [tex]$w = 15$[/tex] pounds:
[tex]$$
\text{dose}_{\text{tsp}} = \frac{15}{2.2} \times 0.2 \approx 1.3636 \text{ teaspoons}.
$$[/tex]
Rounding upward gives:
[tex]$$
1.50 \text{ teaspoons}.
$$[/tex]
3. For [tex]$w = 30$[/tex] pounds:
[tex]$$
\text{dose}_{\text{tsp}} = \frac{30}{2.2} \times 0.2 \approx 2.7273 \text{ teaspoons}.
$$[/tex]
Rounding upward results in:
[tex]$$
2.75 \text{ teaspoons}.
$$[/tex]
Thus, the required doses in teaspoons for the children weighing 10, 15, and 30 pounds are
[tex]$$
1, \; 1\tfrac{1}{2}, \; \text{and} \; 2\tfrac{3}{4} \text{ teaspoons, respectively}.
$$[/tex]
This corresponds to option A.
[tex]$$
\text{dose}_{\text{mg}} = \frac{w}{2.2} \times 40.
$$[/tex]
Since the drug comes in a formulation of 200 mg in 5 mL, its concentration is
[tex]$$
\frac{200 \text{ mg}}{5 \text{ mL}} = 40 \text{ mg/mL}.
$$[/tex]
To convert the milligram dose to a volume in milliliters, we use
[tex]$$
\text{dose}_{\text{mL}} = \frac{\text{dose}_{\text{mg}}}{40}.
$$[/tex]
Knowing that 1 teaspoon equals 5 mL, the corresponding dose in teaspoons is
[tex]$$
\text{dose}_{\text{tsp}} = \frac{\text{dose}_{\text{mL}}}{5} = \frac{\text{dose}_{\text{mg}}}{200}.
$$[/tex]
Substitute the expression for [tex]$\text{dose}_{\text{mg}}$[/tex]:
[tex]$$
\text{dose}_{\text{tsp}} = \frac{\frac{w}{2.2} \times 40}{200} = \frac{w}{2.2} \times \frac{40}{200} = \frac{w}{2.2} \times 0.2.
$$[/tex]
Now, we calculate the dosage for each given weight and then round upward to the nearest [tex]$\frac{1}{4}$[/tex] teaspoon.
1. For [tex]$w = 10$[/tex] pounds:
[tex]$$
\text{dose}_{\text{tsp}} = \frac{10}{2.2} \times 0.2 \approx 0.9091 \text{ teaspoons}.
$$[/tex]
Rounding upward to the nearest quarter teaspoon, we get:
[tex]$$
1.00 \text{ teaspoon}.
$$[/tex]
2. For [tex]$w = 15$[/tex] pounds:
[tex]$$
\text{dose}_{\text{tsp}} = \frac{15}{2.2} \times 0.2 \approx 1.3636 \text{ teaspoons}.
$$[/tex]
Rounding upward gives:
[tex]$$
1.50 \text{ teaspoons}.
$$[/tex]
3. For [tex]$w = 30$[/tex] pounds:
[tex]$$
\text{dose}_{\text{tsp}} = \frac{30}{2.2} \times 0.2 \approx 2.7273 \text{ teaspoons}.
$$[/tex]
Rounding upward results in:
[tex]$$
2.75 \text{ teaspoons}.
$$[/tex]
Thus, the required doses in teaspoons for the children weighing 10, 15, and 30 pounds are
[tex]$$
1, \; 1\tfrac{1}{2}, \; \text{and} \; 2\tfrac{3}{4} \text{ teaspoons, respectively}.
$$[/tex]
This corresponds to option A.
