A20 kg dog requires a 200 mg dose of a drug. a solution contains 90 mg of the drug per tsp. how many milliliters of the solution should be administered to give a dose of 200mg?

  10.95 mL

Step-by-step explanation:

The volume of solution is proportional to the amount you want to administer, so you have ...

  dose/(200 mg) = (1 tsp)·(4.92892 mL/tsp)/(90 mg)

Multiplying by 200 mg, we get

  dose = 200·1·4.92892/90 ≈ 10.953 mL

About 10.95 mL of the solution should be administered to give a dose of 200 mg.

Comment on the conversion factor

1 tsp = 231/768 cubic inches = 4.92892159375 mL exactly

The value is often rounded to 5 mL for cooking purposes. Using that value here would make the dose be 11.11 mL, about 3 mg of drug more than desired.