It's been such a long time since I was in school that I can't remember whether the problem I am dealing with would be classed as Algebra or whether it would belong in another category so please forgive me if this is not the right forum. This is also my first post here.
I am trying to create a formula that will express a calculation that involves data collection so I suspect this might be PreCalculus, which I remember almost failing my freshman year of college (fall of 1976). Possibly I had a bad teacher as up until then I had always done very well in math. The formula that I am looking for is complex and probably has sub-formulas, so I will describe the situation rather than jumping into my version of it. Please move this post to the appropriate forum.
Situation: I want to award a group of people for doing various good behaviors. I've divided these up into twelve tasks or activities I can measure. Each time they do one of these activities I assign certain points. I call each task an "activity" so I've assigned it the symbol A. And each of the tasks has a sub name. So, for instance, would represent the performance of the first type of task.
To even communicate this idea is hard for me because I would like to be able to also represent multiple performances of the same type of task. So, for instance, might be the first time that type of activity is done and the second time. I am afraid to express it this way though, because, from my recollection, to place a number next to a letter means to multiply it. Here I am simply wishing to represent it. (And, of course, the second challenge will be learning Latex so I can communicate with you here in the first place).
In any event, let me describe the situation further. The activities are performed by many people in many locations. Each location has several classes: a village (z for zipcode), a city (c), a county (a for area), a state (s), a region (r), a nation (n) and the globe (g).
I wish to designate a specific dollar amount for each of these location classes that I will distribute to qualifying participants.
I wish to also assign a value, or number of points, to each type of activity that I can change from time to time. Let's call that v, but there would be a v for activities a-z, etc. So I suppose, (am I correct?), that this would be expressed and etc. - the value of activity a, the value of activity b. No?
Next, I want two special types of good behavior- time donated and dollars donated - to be used in the calculation in such a way that the total activity points will be multiplied by the product of a formula that involves these.
The formula is still more complex. There are an unlimited number of charitable organizations. Each of these gets a unique value, (1-7), that is the result of votes by the participants.
The voting process is itself not simply an average score. Each voter has an influence value that is based on another formula. I will get to that formula in some other post. For now, I suppose we could call the influence value i. And we might call the influence value for participant 1 , (though again here, I am concerned that this actually means multiplying rather than representing: please help me disambiguate!).
I am looking for a rating from 1-7 for each charity. I understand what I want but my ability to express mathematical formulas is poor. There is much more to all this but I'll start here. Once a charity has a value, then I want to sum all donations of time and of money to any charity a participant has made, multiply that sum by that value, total all such giving to every charity for that participant, and give that total a name, such as r (for radiance). I will then take the radiance value and compare it with the radiance value of all of the other participants so that I can place their radiance value as compared to others on a curve. The curve will have values from 1-7, just as the charity values will. The curved value I will call the halo effect (H).
To figure out what dollar amount to send each participant I will multiply their total activity points (A) times their halo effect (H) so points (P) are determined P=AH. I will take the dollar amount designated for each location class and distribute it proportionately to each participant in that class. So, say in the zip code 12345 there are 100 participants and the award amount for that zip code is designated as $1000. All participants in that zip code counted together and considered apart from other zip codes have earned halo effect adjusted activity points (P) of 1,000,000.
The formula that I am looking for is the calculation for a single participant. So let's say Tom Smith has P=10,000. That means he has 1% of P for zip 12345. Since the designation is $1000 to be distributed to participants of that zip code he gets an award of $10. How would I express this algebraically for Tom Smith? Tom would then have rewards coming for city, area, county, state, region, nation and globe that would be added together. The result would be Tom's total reward.
I hope I have asked this question in the right place and in a way that is clear. I have a good idea that I would like to implement but I need to communicate it accurately. Thanks in advance for any help.