1st) With a mathematical Rule of Three we can calculate the mL that the patient should take per dose:
![\begin{gathered} 250mg-5mL \\ 500mg-x=(500mg\cdot5mL)/(250mg) \\ \\ x=10mL \end{gathered}](https://img.qammunity.org/2023/formulas/chemistry/college/mrljk4otgx8hlbrbgcsuk2kq1di3n8kvmb.png)
So, the patient should take 10mL of the oral suspension per dose.
2nd) We have to convert the mL to teaspoons, knowing that 1 teaspoon is equal to 5mL:
![\begin{gathered} 5mL-1\text{teaspoon} \\ 10mL-x=\frac{10mL\cdot1\text{teaspoon}}{5mL} \\ \\ x=2teaspoons^{} \end{gathered}](https://img.qammunity.org/2023/formulas/chemistry/college/mnmyqq7btzqzl47f4dlrcspkxtwpkdcnsd.png)
So, the patient should take 2 teaspoons por dose.
3rd) A day has 24 hours, and the patient needs to take the dose every 6 hours, so dividing 24 into 6 we know that the patient must take 4 doses per day.
We know that 1 dose is equal to 2 teaspoons, so:
![\begin{gathered} 1\text{dose}-2\text{teaspoons} \\ 4\text{doses}-x=\frac{4\text{doses}\cdot2\text{teaspoons}}{1\text{dose}} \\ \\ x=8\text{teaspoons} \end{gathered}](https://img.qammunity.org/2023/formulas/chemistry/college/uqxjnotvhkgyq2yeqbzpipaeazzenmv1i5.png)
The patient must take 8 teaspoons per day.