Question

If an intravenous solution containing 123 mg of a drug substance in each 250-mL bottle is to be administered at the rate of 200 μg of drug per minute, how many milliliters of the solution would be given per hour?

Answer 1

24.39mL of the solution would be given per hour.

Explanation:

This problem can be solved by direct rule of three, in which there are a direct relationship between the measures, which means that the rule of three is a cross multiplication.

The first step to solve this problem is to see how many mg of the solution is administered per hour.

Each minute, 200 ug are administered. 1mg has 1000ug, so

1mg - 1000 ug

xmg - 200 ug

`1000x = 200`

`x = (200)/(1000)`

`x = 0.2mg`

In each minute, 0.2 mg are administered. Each hour has 60 minutes. How many mg are administered in 60 minutes?

1 minute - 0.2 mg

60 minutes - x mg

`x = 60*0.2`

`x = 12mg`

In an hour, 12 mg of the drug is administered. In 250 mL, there is 123 mg of the drug. How many ml are there in 12 mg of the drug.

123mg - 250mL

12 mg - xmL

`123x = 250*12`

`x = (250*12)/(123)`

`x = 24.39`mL

24.39mL of the solution would be given per hour.