A doctor needs to administer 2 mL of a 100 mg/mL solution to a 200 lb. patient.

Question

A doctor needs to administer 2 mL of a 100 mg/mL solution to a 200 lb. patient. However, the doctor has the solution available only in 20 mg/mL strength. What volume of the 20 mg/mL solution would be needed to administer the desired dose?

A doctor needs to administer 2 mL of a 100 mg/mL solution to a 200 lb. patient. However, the doctor has the solution available only in 20 mg/mL strength. What volume of the 20 mg/mL solution would be needed to administer the desired dose?

Explanation / Answer

First, we need to keep in mind that the reason the doctor would prefer to administer 2 mL of the 100 mg/mL solution to the patient is because of the amount of mg of drug that would give the patient.

The doctor doesn't have a solution with the desired concentration of drug; the available solution is diluted and only has 20 mg/mL. But the doctor still wants to give the same amount of total mg to the patient. So it will just take more solution to get the amount of mg of drug desired.

First, then, we need to find out how much total drug is desired. After that, we can figure out how much diluted solution it takes to get that total amount of drug.

To find out how much total drug is desired, remember that we would need 2 mL of the more concentrated solution. How much drug would that give us?

2 mL of the more concentrated solution has 100 mg/mL, as the original question tells us. 100 mg/mL means 100 mg in each 1 mL. If there are 100 mg in 1 mL, then 2 mL would have 200 mg.

This means that the doctor wants to administer 200 mg of the drug. Now we need to decide how much diluted solution that will take.

The diluted solution only has 20 mg in each single mL; that's what 20mg/mL means. 20 mg is a lot less than 200 mg. So, how many mL would it take to get up to 200 mg, if we get 20 mg in each 1 mL?

20 mg for the first mL gives us 20 mg total; 20 mg for the second mL gives us 40 mg total; 20 more mg for the next mL gives us 60 mg; and so on.

If you count up by 20 mg at a time, you find you need 10 sets of 20 to reach 200. That means you need 10 mL to get enough sets of 20 mg to total up to 200 mg of drug dose.

(Once you realize you need a bunch of 20's to reach 200, you could just divide 200 by 20 to see how many 20's fit in. Again, it's 10.)

Okay, so we need 10 mL of the diluted solution to reach our desired total of 200 mg of drug dose. That's answer D 10 mL.

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