If a patient needs 10 mg of cough syrup and the concentration is 5 mg/5 mL, how many total mL will be needed?

To determine the total volume of cough syrup needed for a dose of 10 mg, it is essential to understand the concentration of the syrup. The concentration provided is 5 mg per 5 mL, which means that for every 5 mL of syrup, there are 5 mg of the active ingredient.

To find out how much syrup is needed for a 10 mg dose, we can relate the required amount (10 mg) to the concentration. Since 5 mg is contained in 5 mL, we can calculate how many mL will provide 10 mg by setting up a proportion based on the concentration:

1. First, note that 10 mg is double the amount in 5 mg. Thus, we will need double the volume of syrup to get the corresponding active ingredient.
2. Since 5 mL contains 5 mg, to obtain 10 mg we will need 10 mL (as 5 mL for 5 mg x 2 equals 10 mL for 10 mg).

Therefore, the patient would need a total of 10 mL of cough syrup to obtain the desired 10 mg of the medication. This calculation clearly aligns with the concentration provided, leading to the conclusion that