need algebraic formula help

[Perris Calderon]

here's the problem, which I can obviously solve through trial and error but I want to see if there's a formula that solves the problem

a+b=19859 where b = a x .08625

here's where the formula comes from;

the buy out on my car is 19859 which includes tax, I would like to know the number before tax, tax is 8.625%

so I don't need the formual I need to know the process for arriving at the solution

'[edit]

got it, tax is not .08625 it's 1.08625

problem solved, I just devide the final number by tax as 1.08625 and I'm good

 

[fitz]

actually, tax is still .08625 -while the way you solved it is the proper way to solve it, it always helps to see the reason you do that.. you're not really dividing it by tax as 1.08625, your solving for "a"

The solution actually goes:

19859 = a + b

but since b = a * .08625 (or, b = .08625a) then:

19859 = a + 08625a
19859 = a(1 + .08625)
19859 = a(1.08625)

so 19859/1.08625 = a

 

[Perris Calderon]

actually, tax is still .08625 -while the way you solved it is the proper way to solve it, it always helps to see the reason you do that.. you're not really dividing it by tax as 1.08625, your solving for a

The solution actually goes:

19859 = a + b

but since b = a * .08625 (or, b = .08625a) then:

19859 = a + 08625a
19859 = a(1 + .08625)
19859 = a(1.08625)

so 19859/1.08625 = a

nice, thanx for the explanation!

but where did you get "1" from?