Question

an anti - inflammatory drug at a dosage of 1.6 mg/kg is ordered for a child weighing 79.2 lbs. the drug is available at a concentration of 130 mg/3 ml. complete parts a through c. recall that 2.2 lbs = 1 kg
a) what is the child’s weight in kg?
36 kg (type an integer or a decimal.)
b) what is the dosage in milligrams for this child?
57.6 mg (type an integer or a decimal.)
c) how many ml should be administered to the child?
□ ml (round to three decimal places as needed.)

Explanation:

Step1: Find the concentration per mL

The drug concentration is \(130\) mg per \(3\) mL, so the concentration \(C\) (mg/mL) is \(\frac{130}{3}\) mg/mL.

Step2: Use dosage to find volume

We know the dosage needed is \(57.6\) mg (from part b). Let \(V\) be the volume in mL. Using the formula \( \text{Dosage} = C\times V\), we can solve for \(V\): \(V=\frac{\text{Dosage}}{C}\). Substituting the values, \(V = \frac{57.6}{\frac{130}{3}}\).

Step3: Calculate the volume

First, simplify \(\frac{57.6}{\frac{130}{3}}=57.6\times\frac{3}{130}\). Calculate \(57.6\times3 = 172.8\), then divide by \(130\): \(\frac{172.8}{130}\approx1.329\) (rounded to three decimal places).

Answer:

\(1.329\)