Help with Chemistry Problem (math)! Help me please.?

An infant ibuprofen suspension contains 100 mg/ /5.0 mL suspension. The recommended dose is 10 mg/kg body weight. How many mL of this suspension should be given to an infant weighing 17 lb? (Assume two significant figures.)

Please show me your work because I want to understand it! Thank you so much for your help!


The thing that makes this problem tricky is the baby is weighed in pounds while the dosage is given in metric.

So first convert the weight of the baby.

1kg = 2.2 lb

change that into a useful conversion factor by dividing both sides by 2.2 lb.

1kg / 2.2 lb = 1

Now multiply that conversion factor times the 17 pound baby.

1kg / 2.2 lb times 17 lb = 7.72 kg

(note that the lb units cancel)

The dose needed is in mg per kg, so multiply the weight of the baby times dosage

7.72 kg times 10mg/kg = 77.2 mg

(note that the kg units cancel)

So the kid needs 77.2 mg.

The syrup has 100 mg/5ml.

we cant multiply this factor times the baby's weight because we'd have mg squared over ml. So divide by the factor.

division by a factor is the same as multiplying by the inverse.

77.2 mg times 5ml/100 mg = 3.86 ml.

round to 2 decimal places, 3.9 ml.