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 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 December 6th, 2018, 03:45 AM #1 Newbie   Joined: Dec 2018 From: UK Posts: 2 Thanks: 0 Help with deriving formula Can you help to derive a formula that can calculate b2, b3, b4 where T = a1(b1) + a2(b2) + a3(b3) + a4(b4) a1=a2=a3=a4=0.25 b1+b2+b3+b4=1 b1
 December 6th, 2018, 04:53 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,634 Thanks: 2080 y = T = a1(b1) + a2(b2) + a3(b3) + a4(b4) = 0.25(b1 + b2 + b3 + b4) = 0.25, not 2. December 6th, 2018, 06:28 AM   #3
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Quote:
 Originally Posted by adam2018 Can you help to derive a formula that can calculate b2, b3, b4 where T = a1(b1) + a2(b2) + a3(b3) + a4(b4) a1=a2=a3=a4=0.25 b1+b2+b3+b4=1 b1
First, your example makes no sense.

Second, your notation is far more complex than it needs to be.

Third, if you are asking for a solution of the following system

$d + p + q + r = 1, \text { and } d < p < q < r.$

Once d is given, you have three unknowns, but only one equation. No unique solution is possible. If, however, you stipulate that

$0 \le d < 0.25 = \dfrac{1}{4}$, you can bound p, q, and r.

EDIT: Perhaps you are trying to work with this system.

$0 < y,\ 0 \le 4x < y, \ p = \dfrac{x}{y},\ p + q + r + s = 1, \text { and } p < q < r < s.$

If x and y are given, p is determined, q, r, and s are bounded, and

$y = py + qy + ry + sy.$

Last edited by JeffM1; December 6th, 2018 at 07:06 AM. Tags deriving, formula Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Mr Davis 97 Pre-Calculus 11 August 17th, 2014 09:05 AM harley05 Differential Equations 1 April 10th, 2014 02:44 AM alan0354 Applied Math 18 July 27th, 2013 01:02 PM Laurier FMATH BBA Applied Math 1 November 10th, 2011 01:24 PM Wevans2303 Advanced Statistics 0 October 30th, 2011 01:07 PM

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