The dose of a drug is critical. Too small a dose may not treat a patient effectively, while too much can cause serious side effects. A nurse must give a patient 25 $\mathrm{mg}$ of a drug for each kilogram of the patient's mass. If a patient weighs $220 \mathrm{lb}$, how many milligrams of the drug should be given? Use $1 \mathrm{~kg}=2.2 \mathrm{lb}$ and do not round any computations. mg X 5
Solution
Step 1 ：Convert the patient's weight from pounds to kilograms using the conversion factor 1 kg = 2.2 lb. The equation is \(220 \, \text{lb} \times \frac{1 \, \text{kg}}{2.2 \, \text{lb}}\). The lb units cancel out, leaving us with \(\frac{220}{2.2} = 100 \, \text{kg}\).
Step 2 ：Find out how many milligrams of the drug should be given. The nurse must give 25 mg of the drug for each kilogram of the patient's mass. The equation is \(100 \, \text{kg} \times 25 \, \text{mg/kg}\). The kg units cancel out, leaving us with \(100 \times 25 = 2500 \, \text{mg}\).
Step 3 ：Check the work by substituting the values back into the original problem: \(25 \, \text{mg/kg} \times 100 \, \text{kg} = 2500 \, \text{mg}\).
Step 4 ：So, the patient should be given \(\boxed{2500 \, \text{mg}}\) of the drug.
