
Jason A. answered 09/21/20
Chemical Engineering Graduate Offering Tutorship In Person and Online
Hi there James!
This question deals with unit conversions, thus using different rates to get the answers you need.
If you're unfamiliar with cancelling with multiplying and dividing, here's how that works:
Looking at 2 * (3 * 5 / 2), you can cancel both 2's because 2 divided by 2 is just 1 and be left with 3 * 5.
Likewise, if it was 4 * (3 * 5 / 2), you can turn that into 2 * 2 * 3 * 5 / 2 and be left with 2 * 3 * 5.
It saves you work to cancel when you can, and cancelling works the same with units!
In this problem, we are given the following rates:
25 mg / 1 kg body weight / 1 day
2 doses / 1 day
What we need is mg / dose. So, let's set up the equation:
25 mg * 1 day * 23 kg = 287.5 mg
1 kg * 1 day 2 doses 1 dose
The days cancel out because "day" divided by "day" equals 1, and same with the kilograms. Notice that the rate of 2 doses per day is flipped so that we can cancel the units and get where we need to go with the numbers.
You don't need to write the 1's, of course, but the idea is that a patient would may take their doses for 1 day or 30, but they will take 2 doses each 1 day. It's good to be thorough with the 1's because sometimes rates could be given in any way, like 35 per 12 or something, and you want to make sure to catch that for the calculations.
Hope this helps! Please reach out with any further questions!