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

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The equation (AB+1)/(CBA+A+B)=0.138 presents a challenge due to having three unknowns and only one equation. To find specific values for A, B, and C, additional equations are necessary, or assumptions must be made to reduce the variables. One approach discussed is isolating A in terms of B and C, leading to a formula A = (0.138C - 1)/(B - 0.138ABC - 0.138). Another interpretation suggests treating AB as a two-digit number, yielding a unique solution of A=6, B=8, and C=4. Ultimately, without more context or equations, precise values cannot be determined.
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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 dependant 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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