Date: 08/21/99 at 20:33:53 From: Eric Smith Subject: Problems with units I'm having trouble finding information on how to solve problems with units, such as physics or chemistry problems. Specifically, I don't know how to solve "Young's formula" for calculating a child's dose of medicine based on the adult dose. C = A( g / g + 12) where A = adult dose in mg g = child's age For example, if adult dose is 600 mg and child's age is 3 years, what is C? This sounds so easy, but it's driving me crazy. C = 600 mg (3 yr / 3 yr + 12) C = 1800 mg * yr / 3 yr + 12 Now what? Thanks.
Date: 08/22/99 at 23:27:16 From: Doctor Peterson Subject: Re: Problems with units Hi, Eric. Surprisingly, this is a fascinating question, because I can see how you can get hung up on this even though it really is a simple problem. You're being too conscientious, in a sense, and you have hit upon a conflict between two ways of presenting formulas that I hadn't thought about before. It looks like you've learned to carry the units along in the calculation, which is a great method that I like to use. You just have to be careful that the formula is set up right before you use this method, something I don't think I've ever heard taught. First, we have to be clear what the formula is. Parentheses would have been helpful. Here's what I think it should be: g C = A * ------ g + 12 Second, because there is an unlabeled constant in the formula, before we can replace the variables with labeled values, we need to label the constant. The formula was written with a different convention in mind, namely that each variable is expected to be a number representing a _fixed unit_; I would write it carefully like this: g C = A * ------ g + 12 where A = adult dose in mg g = child's age in years C = child's dose in mg To work the problem this way, as intended, you simply plug in the numbers and apply the specified unit at the end: For A = 600 and g = 3: 3 3 C = 600 * ------ = 600 * -- = 120 mg 3 + 12 15 To work this problem with units attached to the numbers, we have to recognize that since g is assumed to be in years, 12 must be in years: g C = A * --------- g + 12 yr where A = adult dose g = child's age C = child's dose Written this way, we could use any units for A and g, and will get an answer for C that is correct in whatever units it ends up with, including any conversions you want to do: For A = 600 mg and g = 3 yr: 3 yr 3 yr C = 600 mg * ------------ = 600 mg * ----- = 120 mg 3 yr + 12 yr 15 yr If g were in days, you would find it necessary to convert it to years before adding; if A were in pounds, you would get C in pounds. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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