My Math Forum  

Go Back   My Math Forum > High School Math Forum > Elementary Math

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


Reply
 
LinkBack Thread Tools Display Modes
December 6th, 2018, 04:45 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<b2<b3<b4
b1 = x1
T = y

For example, one solution is b1=16%, b2=26%, b3=46% for
Y = 2 and x1=12%
2 = 0.25(12%) + 0.25(16%) + 0.25(26%) + 0.25(46%)

How to calculate b2, b3, b4 be when
Y = 2 and x1 =14%
2 = 0.25(14%) + 0.25(?) + 0.25(?) + 0.25(?)
adam2018 is offline  
 
December 6th, 2018, 05:53 AM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 19,986
Thanks: 1853

y = T = a1(b1) + a2(b2) + a3(b3) + a4(b4) = 0.25(b1 + b2 + b3 + b4) = 0.25, not 2.
skipjack is offline  
December 6th, 2018, 07:28 AM   #3
Senior Member
 
Joined: May 2016
From: USA

Posts: 1,210
Thanks: 497

Quote:
Originally Posted by adam2018 View Post
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<b2<b3<b4
b1 = x1
T = y

For example, one solution is b1=16%, b2=26%, b3=46% for
Y = 2 and x1=12%
2 = 0.25(12%) + 0.25(16%) + 0.25(26%) + 0.25(46%)

BUT THIS IS NOT TRUE.

0.25 * 0.12 = 0.03.

0.25 * 0.16 = 0.04.

0.25 * 0.26 = 0.065.

0.25 * 0.46 = 0.115.

0.03 + 0.04 + 0.065 + 0.115 = 0.07 + 0.18 = 0.25.

And one quarter does not equal 2.

How to calculate b2, b3, b4 be when
Y = 2 and x1 =14%
2 = 0.25(14%) + 0.25(?) + 0.25(?) + 0.25(?)
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 08:06 AM.
JeffM1 is offline  
Reply

  My Math Forum > High School Math Forum > Elementary Math

Tags
deriving, formula



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Deriving the formula for summing a sequence of squares Mr Davis 97 Pre-Calculus 11 August 17th, 2014 10:05 AM
deriving equations harley05 Differential Equations 1 April 10th, 2014 03:44 AM
Help deriving this Bessel function formula alan0354 Applied Math 18 July 27th, 2013 02:02 PM
Deriving a closed newton-cotes formula for n = 3 Laurier FMATH BBA Applied Math 1 November 10th, 2011 02:24 PM
Deriving formula from tree diagram? Wevans2303 Advanced Statistics 0 October 30th, 2011 02:07 PM





Copyright © 2018 My Math Forum. All rights reserved.