Question

A mother calls you to ask about a proper dosage of cough medicine for her 2-year-old. The bottle says to administer 5.0mg/kg three times a day for children under 3 years of age. The cough syrup is supplied in a liquid that contains 50.0mg/mL. How many teaspoons of cough syrup should she give the child, who weighs 26 lb , in each dose?
Express your answer using two significant figures.

Answer 1

some conversion factors we'll need to use for this problem:

1 lb = 0.454 kg
1 mL = 0.203 teaspoons

let's start with 26lb. multiplying this by 0.454 kgs/lb will convert the child's weight to kg. from there, multiply by 5.0mg/kg to get the dose in mg. from there, you can divide by 50.0mg/mL to get the volume in mL. finally, multiply the volume in mL by 0.203tsp/mL to get the volume in teaspoons.

we can set up the conversion like so:

\[\frac{ 26~lb }{ }\frac{ 0.454kg }{ 1~lb }\frac{ 5.0mg }{ 1~kg }\frac{ 1~mL }{ 50.0mg }\frac{ 0.203~tsp}{ 1~mL }\]notice how the units cancel out and we're left with teaspoons. round the result to 2 sig figs as stated.