I was taught - and I teach - to do this by "dimensional analysis"
Assuming you know that 1kg = 2.2 lbs, 60 minutes = 1 hour, and 1000mcg = 1mg and 1g = 1000 mg
To use 'dimensional analysis' you have to have everything equal to something else in the problem, so for #1, the order is 4mg / minute and the concentration is 2 grams in 1000mL
1. 4mg 1g 1000mL 60 min
min 1000 mg 2g 1 hour
154lbs 1kg 15mcg 1mg 500mL
pt. 2.2 lbs kg min 1000mcg 800 mg
gives answer in ml/ hour (which is a pump rate)
lbs on top cancels lbs on bottom, etc - all thats left is ml/hour, multiply across the top and bottom, divide,
5mcg 1mg 500mL 60 minutes
minute 1000mcg 50 mg 1 hour
again leaves answers in mL/ hour
6mL 2g 1000 mg
hour 500 mL 1g
This will give you mg/hour if you want mg/min, multiply by 1 hour
5. Weight is thrown in there to make you NUTS - it doesn't matter in this problem.
25mL 900 mg
hour 500 ML
again, this gives you mg / hour - if you want it per minute, see above.
6. Your patient is to start a dopamine drip due to severe hyptotension. The pharmacy has sent you a 250ml bag of NS with 400mg dopamine. What is the rate of infusion if the physician has ordered the following: 8mcg/kg for your client that weighs 186 pounds?
186 lbs 1kg 8mcg 1mg 250mL
patient 2.2lb kg (per hour?) 1000mcg 400mg
7. How much would the patient be receiving if his pump was running at 11ml/hr?
I got 17.6/hr???
hour 250 mL = 17.6 mg/hour if you want to take that all the way to weight dosage, though
11mL 400mg 1000mcg patient 2.2lb
hour 250 mL 1 mg 186lbs 1kg
then the patient is receiving 208 mcg/kg, so it kind of depends on exactly what the teacher is asking.
My head hurts, and all this formatting is making it worse. If you would like me to check your answers, send me a message so I get an email. It seems like you're on the right track, though.
And YES - nurses really do have to do this kind of math. You do get to use a calculator, usually, but the set up is all you.