Splitting a margin evenly between a number

[CharlesW]

Hello Everybody,

I wanted to split a margin (say, 15%) evenly between a number (say, 3,000) so that the same value is split above and below 3,000 and the lower number is 15% lower than the higher number. I think I've done this right but wanted to ask the smart folks here just to be sure:

If x = the distance between 3,000 and the topside of the 15% margin, then x=3,000+x. Since 0.85(3,000+x)=3,000-x, we solve for x:

= 0.85(3,000+x) = 3,000-x
= 2,550+0.85x=3,000-x
= x+0.85x=3,000-2,550
= x(1+0.85)=450
= 1.85x=450
= x=450/1.85
= x=243.2432


Confirming:


0.85*3,243.2432 = 3,000-243.2432 [?]


2,756.75 = 2,756.75

Is this correct? If so, is it the best way to go about it. The reason I ask is that, when I tried it the first time, I took 15% of 3,000 (.15*3,000) = 450 and thought I could split 450 above and below 3,000, or between 3,225 and 2,775. But then I found that 0.85*3,225 = 2,741.25, so 2,775 is not 15% below 3,225. Drawing a picture helped me visualize it and led me to the above solution. I wonder if I went about it right?

Many thanks

 

[CharlesW]

Many thanks Denis.

 

[CharlesW]

A better way (What a Dummy I am)

Looks good to me.

40% "around" 3000 ?

1.4(3000 - x) = 3000 + x
4200 - 1.4x = 3000 + x
2.4x = 1200
x = 500

3500 : 3000 : 2500

Yes?

Denis-Sensei, are you still there?

Boy, what a dummy I am. I was going about it all wrong. I think I found a better way (and immediately thought of King Richard III's retort to Lord Stanley, "What need'st thou run so many miles about when thou mayst tell they tale the nearest way?").

If M is the median between two numbers, the second of which is 15% below the first, I'd wanted to find a formula that gave b for any value of M:

b
|
M
|
0.85b

M is equal to b minus half the distance between b and 0.85b, or

M = b-(b-0.85b)/2

Solving for b,

M = b-b(1-0.85)/2
M = b-0.15b/2
M = (2b-0.15b)/2
M = b(2-0.15)/2
M = 1.85b/2
2M = 1.85b
b = 2M/1.85

Checking with M = 3,000 as before:

b = 2(3,000)/1.85 [?]
b= 6,000/1.86
b = 3,243.24320.85b = 2,756.7567

I assume this is the best approach?

This struck me in the haze of waking up this morning.