Another Chemistry Question

At a dosage of 20 micro/kg body weight,
(i) how many milligrams of dosage should a 78kg patient receive?
(ii) how many milligrams of dosage should a 160lb patient receive?
( 1kg=2.2046lb)

(1) 78kg = 78000g
20microgram = 20 x 10^-6g = 2 x 10^-5g
Dosage to a 78kg patient = 78000 x 2 x 10^-5g = 1.56g = 1560mg

(2) 160lb = (1/2.2046) x 160 kg = 72.57kg
Dosage to a 72.57kg patient = 72570 x 2 x 10^-5g = 1.451g = 1451mg

(i) Ok, lets say your micro is in kg. Then one kg = 1,000g. Our dosage however is 20 micro per kg for a 78kg patient.
Thus, 1 micro= 1*10^(-6).
Now a 78kg patient = 78 * 1000g = 78,000g
Now 20 micro gram=0.00002g per 1000g.
If 2*10^(-5) goes for 1000g, then X goes for 78,000g.
Thus, X=78,000g * 0.00002/1000g= 0.00156 = 1560 micro.
So the dosage would be 1560micro to a 78kg patient.
And 1 micro kg = 1 milligram. As 0.000001micro kg or milligram = 1kg. Thus the patient will be administered 1,560mg of drug.
(ii) now for a 160Ibs patient, one 1kg = 0.000001micro= 2.2046Ibs.
160Ibs = xkg. Thus x = 160Ibs * 1kg/2.2046Ibs = 72.5kg.
But 20micro kg(20 milligrame)= 1kg. Thus xmg=72.5kg.
Therefor, x=72.5kg * 20mg/1kg= 1451mg. Are U now satisfied?