Questions: For each kilogram of a person's weight, 2.5 milligrams of a drug is to be given. What dosage should be given to a child who weighs 93 pounds? Use milligrams is the proper dosage for a child that weighs 93 pounds. (Round to the nearest hundredth as needed.)

For each kilogram of a person's weight, 2.5 milligrams of a drug is to be given. What dosage should be given to a child who weighs 93 pounds? Use milligrams is the proper dosage for a child that weighs 93 pounds. (Round to the nearest hundredth as needed.)

Transcript text: For each kilogram of a person's weight, 2.5 milligrams of a drug is to be given. What dosage should be given to a child who weighs 93 pounds? Use $\square$ milligrams is the proper dosage for a child that weighs 93 pounds. (Round to the nearest hundredth as needed.)

Solution

Solution Steps

Step 1: Convert the weight from pounds to kilograms

To convert the weight from pounds to kilograms, we use the formula: $W_{kg} = W_{lb} \times C$. Given that the weight in pounds ($W_{lb}$) is 93 and the conversion factor ($C$) is 0.454, we calculate the weight in kilograms ($W_{kg}$) as follows: $$W_{kg} = 93 \times 0.454 = 42.184 \text{ kg}$$

Step 2: Calculate the total dosage

Using the dosage rate ($D$) of 2.5 mg/kg and the weight in kilograms ($W_{kg}$) calculated in Step 1, we calculate the total dosage to be administered as follows: $$\text{Total Dosage} = D \times W_{kg} = 2.5 \times 42.184 = 105.460 \text{ mg}$$ After rounding to the nearest 2 decimal places, the total dosage to be administered is 105.46 mg.