Algebra Question: What Is the Formula for This Problem

Factual Questions
1

Say Alice makes $50 and pays $25 in taxes, and Bob makes $1,000 and pays $125 in taxes. If the amount of taxation changes at a constant rate, what would be the formula for determining the proper amount of taxation for any income?

2

Homework?

3

T = mx + b

25 = 50x +b
125 = 1000x + b

4

Not to Junior Mod or anything, but isn’t there a rule against asking for answers to homework problems on the SDMB?

5

I swear, this isn’t homework. If I’d actually done my homework when I was in algebra class 17 years ago, I probably wouldn’t need to ask.

6

Tax=income*rate + flatamount.

When confused about these things, look to the units. The tax bill is in “tax dollars”, the income is in “income dollars” and the rate is “tax $s per income $s”. “Per” means divide, so you can see that if you put the tax over the income, the units match the rate’s unit. So slap those on one side of the equal sign and the rate on the other. Solve for the unknown variable.

When I’m on a long trip, I like to calculate time to the next exit (or whatever) when a sign says it’s, like, 30 miles away. I say to myself “Distance is in miles, time in minutes, and speed in mph/60minutes, so D/M=mph/60” because it’s “miles/minutes=miles/minutes”. Hope this helps.

7

[QUOTE=IntelSoldier]
Tax=income*rate + flatamount./QUOTE]

Thanks. What’s got me stumped now is how I calculate the rate since it’s variable depending on the income. I know that at $50, the rate is 50% and at $1,000 it’s 12.5%. Since it changes at a constant rate, how do I figure out what it would be at $500?

8

Use linear interpolation – find out what line crosses through both of those points.

9

Either you’re misinterpreting IntelSoldier’s point, or everyone else is misinterpreting your question.

Starting from the top:

  1. You asked, “what would be the formula for determining the proper amount of taxation for any income?”
  2. I assume you’re asking, “how does one determine the number of dollars paid in taxes, given an income?” (as opposed to, “how does one determine the the percentage of one’s income paid in taxes?”)
  3. You say that “the amount of taxation changes at a constant rate”.
  4. All this boils down to a classic ninth grade algebra problem: Given two points, find the equation of the line through them. Your two points are (50, 25) and (1000, 125). It would probably help if you drew this out on a piece of paper.
  5. The standard equation of a line is y = m*x + b, where x and y are the two things you’re graphing (income and tax, in your case), m is the slope, and b is the y-intercept.
  6. To expand on 5 in your case: In your setup, everyone pays some tax, even the people that make zero income. That’s the “flatamount” IntelSoldier was referring to. That’s also the “y-intercept”. If you make more that $0, you also pay an additional amount based on your income. That’s the “rate” IntelSoldier was referring to. That’s also the slope.
  7. So, y = mx + b; tax = mincome + b; tax = rate*income + flatamount.
  8. The “rate” changes linearly; i.e., rate = (125-25)/(1000-50)
  9. The “flatamount” can then be calculated by dropping the “rate” into the equation.
10

Them’s some queer numbers though - the answer doesn’t come out anything like tidily. (Also, Alice is getting screwed by the system.)

11

No doubt, it’s the former. I appreciate your thoroughness and patience. The difficulty I was having is the applying of the information everyone’s provided so I can plug it into Excel.

Thank you vary much for the through answer.