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
To solve this problem, we need to convert the given information into the desired unit, which is the number of capsules per dose. Here's how you can do it step by step:
1. Start with the given rate: 0.003 mg of the drug per pound per day.
2. To eliminate the unit of pounds, multiply by the weight of the person, which is 160 pounds. This gives us (0.003 mg * 160 lb) / day.
3. Since we want to find the number of capsules per dose, we need to eliminate the unit of days. We know that the drug should be taken 3 times a day, so multiply by 1 day / 3 times. This gives us (0.003 mg * 160 lb * 1 day) / (day * 3 times).
4. Simplify the units by canceling out the common units. The pounds cancel out, as well as the days, leaving us with (0.003 * 160 mg) / 3 times.
5. Now, we need to eliminate the unit of milligrams since we know that each capsule contains 0.010 mg of the drug. Multiply by 1 capsule / 0.010 mg. This gives us (0.003 * 160) / (3 times * 0.010) capsules.
6. Simplify the calculation to obtain the final answer: (0.003 * 160) / (0.030) capsules.
7. Calculate the result: 0.0064 capsules.
Therefore, Bryson should take approximately 0.0064 capsules per dose to achieve the desired dosage of the cholesterol-lowering drug.