Do This Algebra in Excel?

[Excelage]

Hi,

How could I use *just* formulas to solve for "X" in the following algebra equation in Excel?

(58.9806-x)/(195.3-x) = .1

Thank you in advance for any assistance.

 

[joeu2004]

Enter the following formula into A1:

=(58.9806-B1)/(195.3-B1)

Then use Goal Seek or Solver to set A1 to 0.1 by changing B1.

Note that with default options, both result in only an approximate value in B1: 43.8226762300783 for Goal Seek; and 43.833967324864 for Solver.

But by changing Excel Options > Formulas > Maximum Change (under Enable Iterative Calculation) to 0.00000000001, Goal Seek finds the exact solution: 43.834.

(It is not necessary, and it is ill-advised, to actually enable Iterative Calculation.)

I use Excel 2010. YMMV.

PS.... The exact solution is B1 = (58.9806 - 19.53) / (1 - 0.1) .

 

[Macropod]

More precisely, x = 43.834, thus:
(58.9806-x)/(195.3-x) = .1
(589.806-10x)/(195.3-x) = 1
589.806-10x = 195.3-x
394.506 = 9x
43.834 = x

So, if you put:
=(58.9806-B1)/(195.3-B1)
in A1 and:
43.834
in B1, A1 will return:
0.1

 

[Excelage]

Enter the following formula into A1:

=(58.9806-B1)/(195.3-B1)

Then use Goal Seek or Solver to set A1 to 0.1 by changing B1.

Note that with default options, both result in only an approximate value in B1: 43.8226762300783 for Goal Seek; and 43.833967324864 for Solver.

But by changing Excel Options > Formulas > Maximum Change (under Enable Iterative Calculation) to 0.00000000001, Goal Seek finds the exact solution: 43.834.

(It is not necessary, and it is ill-advised, to actually enable Iterative Calculation.)

I use Excel 2010. YMMV.

PS.... The exact solution is B1 = (58.9806 - 19.53) / (1 - 0.1) .

Thank you, but how do I solve it without solver or goal seek? I need to use just cell references. Thanks again for any help.

 

[Excelage]

More precisely, x = 43.834, thus:
(58.9806-x)/(195.3-x) = .1
(589.806-10x)/(195.3-x) = 1
589.806-10x = 195.3-x
394.506 = 9x
43.834 = x

So, if you put:
=(58.9806-B1)/(195.3-B1)
in A1 and:
43.834
in B1, A1 will return:
0.1

Thank you, but I already know to do the algebra on paper. Your Excel solution requires me to already know X but I need to solve for X in Excel without already knowing the solution. I need Excel to do all the math. Thank you for any assistance.

 

[wideboydixon]

Generically:

(a-x)/(b-x)=c ... multiply both sides by b-x
a-x=cb-cx ... add x to both sides
a=x+cb-cx ... subtract cb from both sides
a-cb=x-cx ... refactor right hand side
a-cb=x(1-c) ... divide both sides by 1-c
(a-cb)/(1-c)=x

so, in your case:

Book1
	A	B
1	a	58.9806
2	b	195.3
3	c	0.1
4	x	43.834
Sheet1

Cell Formulas
Range	Formula
B4	=($B$1-$B$2*$B$3)/(1-$B$3)

WBD