Answer :
We are given that the recommended dosage is
[tex]$$40\text{ mg for each }2.2\text{ pounds of body weight},$$[/tex]
divided into three doses each day (taken every 8 hours). In addition, the drug is provided with a formulation of
[tex]$$200\text{ mg per }5\text{ ml},$$[/tex]
and since
[tex]$$5\text{ ml} = 1\text{ teaspoon},$$[/tex]
each teaspoon contains 200 mg of the drug.
For each child's weight, we follow these steps:
1. Calculate the dose in mg per dose:
For a child weighing [tex]$W$[/tex] pounds, the medication per dose (in milligrams) is given by
[tex]$$\text{Dose in mg} = \left(\frac{W}{2.2}\right) \times 40.$$[/tex]
2. Convert the dose from milligrams to teaspoons:
Since each teaspoon contains 200 mg, the dose in teaspoons is
[tex]$$\text{Teaspoons (raw)} = \frac{\text{Dose in mg}}{200}.$$[/tex]
3. Round up to the nearest [tex]$\frac{1}{4}$[/tex] teaspoon:
After computing the raw teaspoons, we round up (i.e. use the minimum amount that is not less than this value) to the next [tex]$\frac{1}{4}$[/tex] teaspoon increment.
Now, let’s apply these steps to the given weights.
---
For 10 pounds:
1. Calculate the dose in mg:
[tex]\[
\text{Dose}_{10} = \left(\frac{10}{2.2}\right) \times 40 \approx 181.82\text{ mg}.
\][/tex]
2. Convert to teaspoons:
[tex]\[
\text{Teaspoons}_{10} = \frac{181.82}{200} \approx 0.91\text{ teaspoons}.
\][/tex]
3. Round up to the nearest [tex]$\frac{1}{4}$[/tex] teaspoon:
The next quarter increment after 0.91 is 1.00 teaspoon.
---
For 15 pounds:
1. Calculate the dose in mg:
[tex]\[
\text{Dose}_{15} = \left(\frac{15}{2.2}\right) \times 40 \approx 272.73\text{ mg}.
\][/tex]
2. Convert to teaspoons:
[tex]\[
\text{Teaspoons}_{15} = \frac{272.73}{200} \approx 1.36\text{ teaspoons}.
\][/tex]
3. Round up to the nearest [tex]$\frac{1}{4}$[/tex] teaspoon:
The next quarter increment after 1.36 is 1.50 teaspoons.
---
For 30 pounds:
1. Calculate the dose in mg:
[tex]\[
\text{Dose}_{30} = \left(\frac{30}{2.2}\right) \times 40 \approx 545.45\text{ mg}.
\][/tex]
2. Convert to teaspoons:
[tex]\[
\text{Teaspoons}_{30} = \frac{545.45}{200} \approx 2.73\text{ teaspoons}.
\][/tex]
3. Round up to the nearest [tex]$\frac{1}{4}$[/tex] teaspoon:
The next quarter increment after 2.73 is 2.75 teaspoons.
---
Thus, the required teaspoons for each of the entries are:
- 10 pounds: 1 teaspoon
- 15 pounds: 1½ teaspoons
- 30 pounds: 2¾ teaspoons
This corresponds to answer option A:
[tex]$$1, \; 1\frac{1}{2}, \; 2\frac{3}{4}.$$[/tex]
[tex]$$40\text{ mg for each }2.2\text{ pounds of body weight},$$[/tex]
divided into three doses each day (taken every 8 hours). In addition, the drug is provided with a formulation of
[tex]$$200\text{ mg per }5\text{ ml},$$[/tex]
and since
[tex]$$5\text{ ml} = 1\text{ teaspoon},$$[/tex]
each teaspoon contains 200 mg of the drug.
For each child's weight, we follow these steps:
1. Calculate the dose in mg per dose:
For a child weighing [tex]$W$[/tex] pounds, the medication per dose (in milligrams) is given by
[tex]$$\text{Dose in mg} = \left(\frac{W}{2.2}\right) \times 40.$$[/tex]
2. Convert the dose from milligrams to teaspoons:
Since each teaspoon contains 200 mg, the dose in teaspoons is
[tex]$$\text{Teaspoons (raw)} = \frac{\text{Dose in mg}}{200}.$$[/tex]
3. Round up to the nearest [tex]$\frac{1}{4}$[/tex] teaspoon:
After computing the raw teaspoons, we round up (i.e. use the minimum amount that is not less than this value) to the next [tex]$\frac{1}{4}$[/tex] teaspoon increment.
Now, let’s apply these steps to the given weights.
---
For 10 pounds:
1. Calculate the dose in mg:
[tex]\[
\text{Dose}_{10} = \left(\frac{10}{2.2}\right) \times 40 \approx 181.82\text{ mg}.
\][/tex]
2. Convert to teaspoons:
[tex]\[
\text{Teaspoons}_{10} = \frac{181.82}{200} \approx 0.91\text{ teaspoons}.
\][/tex]
3. Round up to the nearest [tex]$\frac{1}{4}$[/tex] teaspoon:
The next quarter increment after 0.91 is 1.00 teaspoon.
---
For 15 pounds:
1. Calculate the dose in mg:
[tex]\[
\text{Dose}_{15} = \left(\frac{15}{2.2}\right) \times 40 \approx 272.73\text{ mg}.
\][/tex]
2. Convert to teaspoons:
[tex]\[
\text{Teaspoons}_{15} = \frac{272.73}{200} \approx 1.36\text{ teaspoons}.
\][/tex]
3. Round up to the nearest [tex]$\frac{1}{4}$[/tex] teaspoon:
The next quarter increment after 1.36 is 1.50 teaspoons.
---
For 30 pounds:
1. Calculate the dose in mg:
[tex]\[
\text{Dose}_{30} = \left(\frac{30}{2.2}\right) \times 40 \approx 545.45\text{ mg}.
\][/tex]
2. Convert to teaspoons:
[tex]\[
\text{Teaspoons}_{30} = \frac{545.45}{200} \approx 2.73\text{ teaspoons}.
\][/tex]
3. Round up to the nearest [tex]$\frac{1}{4}$[/tex] teaspoon:
The next quarter increment after 2.73 is 2.75 teaspoons.
---
Thus, the required teaspoons for each of the entries are:
- 10 pounds: 1 teaspoon
- 15 pounds: 1½ teaspoons
- 30 pounds: 2¾ teaspoons
This corresponds to answer option A:
[tex]$$1, \; 1\frac{1}{2}, \; 2\frac{3}{4}.$$[/tex]
