Article View: aus.mathematics
Article #168Re: I need help with these equations
From: Ken Pledger
Date: Thu, 09 Nov 2006 22:34
Date: Thu, 09 Nov 2006 22:34
44 lines
2842 bytes
2842 bytes
In article <zIuVg.18478$vi3.4885@bignews3.bellsouth.net>,
Bill <Bill@hotmail.com> wrote:
> Considering the following table ...
>
> a | b | c | d
> ---------------------
> 256 | 80 | 4 | 0
> 704 | 80 | 11 | 7
> 288 | 512 | 0 | 5
> 736 | 512 | 7 | 12
>
> Given a pair of values for a and b, I derived the following to solve for
> c and d ...
>
> c = ( ( a - 256 ) / 64 ) - ( ( b - 464 ) / 96 )
> d = ( ( a - 256 ) / 64 ) + ( ( b - 80 ) / 96 )
>
> But given a pair of values for c and d, I am having difficulty finding a
> and b. I came up with the following but it is incorrect. any help would
> be appreciated, thank you.
>
> a = ( ( c * 64 ) + 256 ) + ( ( d * 96 ) + 464 )
> b = ( ( c * 64 ) + 256 ) - ( ( d * 96 ) + 80 )
For the last three months I've been too busy to look at news
groups, but you may still like this belated reply.
Your first pair of equations can be simplified to
c = a/64 - b/96 + 5/6
d = a/64 + b/96 - 29/6.
Solving these for a and b gives
a = 32(d + c) + 128
b = 48(d - c) + 272
which you can check do fit the original data in your table.
Ken Pledger.
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