What are the values of A, B, and C in the equation (AB+1)/(CBA+A+B)=0.138?

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Discussion Overview

The discussion revolves around finding the values of the variables A, B, and C in the equation (AB+1)/(CBA+A+B)=0.138. Participants explore the implications of having one equation with three unknowns, discussing potential assumptions and methods for solving the equation.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant notes that to find values for A, B, and C, additional equations are necessary due to the presence of three unknowns in a single equation.
  • Another participant suggests making assumptions to reduce the number of variables, mentioning an attempt to set AB=X without success.
  • A different approach is proposed where one variable is treated as dependent, leading to a formula for A in terms of B and C, provided certain conditions are met.
  • One participant argues that without additional information, it is impossible to find specific values for the variables, suggesting that the best approach is to derive formulas for each variable instead.
  • A later reply introduces an alternative interpretation of the variables, treating AB as a two-digit number, which leads to a unique solution for A, B, and C.

Areas of Agreement / Disagreement

Participants generally agree that additional information or equations are needed to find specific values for A, B, and C. However, there are competing views on how to approach the problem, with some suggesting assumptions and others emphasizing the limitations of the single equation.

Contextual Notes

Participants express uncertainty regarding the assumptions needed to reduce the number of variables and the implications of different interpretations of the equation.

Ravian
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(AB+1)/(ABC+A+C)=0.138, Find values of A,B,C.
 
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Hi, Ravian,

Does that example have more information with it? You show one equation built with three unknown variables. Two more equations are necessary as requirement for finding VALUES for A, B, and C.
 
You are right but this is the way it is. I guess we need to make assumptions to reduce the number of variables. I tried AB=X and some other but it is not working. Fortunately I know it is solvable but I don't know how.
 
If you just need ANY value you can easily do this by letting A=0 and solving for C.

If you need ALL values you just need to treat one variable as a dependent variable, so solving for A in terms of B and C (if I did my algebra right) you get:
A = (0.138C - 1)/(B -0.138ABC - 0.138). So for any B,C provided ABC+A+C ≠ 0

That's as spefic as you can get i believe.
 
Ravian said:
You are right but this is the way it is. I guess we need to make assumptions to reduce the number of variables. I tried AB=X and some other but it is not working. Fortunately I know it is solvable but I don't know how.
Isolate all terms with an “A” to one side, then factor out the “A”. would be a good way to approach this.
 
Ravian said:
You are right but this is the way it is. I guess we need to make assumptions to reduce the number of variables. I tried AB=X and some other but it is not working. Fortunately I know it is solvable but I don't know how.

Nonsense. You only have one equation which uses three variables. You have no other information. You cannot find any values for the variables. The best you can do is solve for each variable to find a formula for each. Otherwise, you cannot solve for any values.
 
Ravian said:
(AB+1)/(ABC+A+C)=0.138, Find values of A,B,C.

without any context behind the question it's reasonable to interpret it in another popular way. although i still don't think it works with this particular question you posted here, but consider the similar type:

(AB + 1) / (CBA + A + B) = 0.138

now instead of treating AB as A multiplied with B, for example, we can interpret it as the integer number with A tens and B units. in this case it has a unique solution:

A = 6, B = 8, C = 4

(68 + 1) / (486 + 6 + 8) = 0.138
 

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