Question

What is the range of acetaminophen dosages, expressed in mg acetaminophen/kg body weight, for children who weigh between 24 and 35 lb?

A children’s pain relief elixir contains 80. mg acetaminophen per 0.50 teaspoon. The dosage recommended for a child who weighs between 24 and 35 lb is 1.5 teaspoons.

Answer 1

The dosage ranges from 15 mg/kg to 22 mg/kg.

Explanation:

Step 1. Calculate the mass of acetaminophen in a dose

`1.5color(red)(cancel(color(black)("tsp"))) × "80. mg"/(0.50 color(red)(cancel(color(black)("tsp")))) = "240 mg"`

Step 2. Convert pounds to kilograms

`24 color(red)(cancel(color(black)("lb"))) × "1 kg"/(2.205 color(red)(cancel(color(black)("lb")))) = "10.9 kg"`

`35 color(red)(cancel(color(black)("lb"))) × "1 kg"/(2.205 color(red)(cancel(color(black)("lb")))) = "15.9 kg"`

Step 3. Calculate the dosage range

`"High dosage" = "240 mg"/"10.9 kg" = "22 mg/kg"`

`"Low dosage" = "240 mg"/"15.9 kg" = "15 mg/kg"`

The dosage ranges from 15 mg/kg to 22 mg/kg.