If someone could figure this problem out and tell me how to do it, i would really appreciate the help!
Bryson needs .003 mg of a cholesterol-lowering drug per pound per day. The drug should be taken 3 times a day. If capsules contain .010 mg of the drug, how many capsules should he take each time? He weights 160 lb.
Let D represent the drug. 0.003 mg of a cholesterol-lowering drug per pound per day looks like this:
0.003 mg D
-----------
lb • day
The wanted unit at the is capsule (cap) of Drug (D) per time.
Start by eliminating the units above. We could eliminate mg, lb, or day. It does not really matter. Let's go with lb. In dimensional analysis or unit factoring, one eliminates unit by placing the subsequent one diagonally. Since lb is in the denominator of our start, we need to place 160 lb in the numerator.
0.003 mg D × 160 lb
-----------
lb • day
This eliminates the lb.
0.003×160 mg D
---------------
day
Now we need to eliminate mg or day. Let's go for the day this time. The drug has to be taken 3 times or doses per day: 3 times/day. Day is in the denominator; we have to put day then in the numerator.
0.003×160 mg D 1 day
-------------- × --------
day 3 times
The days cancel out:
0.003×160 mg D
--------------
3 times
Let's eliminate the mg now. One capsule contains or = 0.010 mg. In this case mg is in the numerator; we need it in the denominator in our final conversion.
0.003×160 mg D 1 cap
-------------- × -------
3 times 0.010 mg
The mg cancels out and we are left with capsules of D per dose (or time if you wanted that instead.) Just finish the math.
We could have got to this with other approaches.
0.003 mg D
-----------
lb • day
We could have eliminated day first instead.
0.003 mg D 1 day
----------- × --------
lb • day 3 times
and so on...
Unfortunately, the spacing did not work out as I had typed it in.
0.003 mg D 1 day
----------- × --------
lb • day 3 times
=
0.003 mg D____ ��1 day
----------- × --------
lb • day ______3 times
with the underscore equaling spaces
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