Question

A cough syrup contains $ 10 $ mg of dextromethorphan hydrobromide per $ 5 $ mL. How many milligrams of the drug are contained in a $ 120 $ -mL container of the syrup?

Answer 1

Hint: A ml is expressed as the unit of liquid which is used in the cough syrup. The contents of the dextromethorphan is $ 10 $ mg per $ 5 $ mL. Place the values in the given $ 120 $ ml of syrup and will use the multiplication to find the required value.

Complete step by step solution:
Now, as we know that $ 5 $ mL contains $ 10 $ mg of dextromethorphan hydrobromide
It can be re-written as –
 $ 5 $ mL cough syrup $ = 10 $ mg of dextromethorphan hydrobromide
Therefore $ 120 $ mL cough syrup?
Do cross multiplication
 $ = \dfrac{{120 \times 10}}{5} $
Find the factor of the term in the numerator part of the above expression.
 $ = \dfrac{{120 \times 2 \times 5}}{5} $
Common factors from the numerator and the denominator cancel each other. Therefore, remove from the numerator and the denominator.
 $ = 120 \times 2 $
Simplify the above expression –
 $ = 240 $ mg
Hence, the $ 120 $ -mL container of the cough syrup contains $ 240 $ mg of dextromethorphan hydrobromide.
So, the correct answer is “ $ 240 $ mg”.

Note: Remember the correlation between the two terms and the contents in the particular relation. Remember the concepts and apply accordingly. You should remember the relation between the two units as it is the base of the solutions.
The units are the standards for the measurement of the physical quantities which needs to be clear to be useful. Units are the internationally accepted standards for measurements of the physical quantities.
Different types of system of units are –
SI (International system of units)
MKS (Meter-kilogram-second) system
CGS (centimetre-gram-second) system