Manny Mo and Jack give away money:

Manny Mo and Jack have 12 billion between them, 4 billion each.

They find this inventor who is a combination of Edison, Keurig and Tesla

and they make him an offer, full partnership and they will give him as much money as they need to make all four of them have the same amount of money.

So what the hell, 1 billion from each, they all have 3 billion and they go home and have a party.

Not so fast, the IRS says.

You gave him 3 billion dollars and the tax on that is 40 % so they take 1.2 billion and leave him with 1.8.

They go, ok, we will all chip in 400 million apiece and pay the tax. The IRS says, the tax on 1.2 billion is 480 million.

So they get their favorite math dude working for the company and he comes up with the right numbers where everyone has the same amount and the IRS is satisfied.

So who pays what to whom? What did everyone receive?

Originally posted by sonhouse
Manny Mo and Jack have 12 billion between them, 4 billion each.

They find this inventor who is a combination of Edison, Keurig and Tesla

and they make him an offer, full partnership and they will give him as much money as they need to make all four of them have the same amount of money.

So what the hell, 1 billion from each, they all have 3 billion ...[text shortened]... he same amount and the IRS is satisfied.

So who pays what to whom? What did everyone receive?

They end up with 18/7 billion each.
IRS gets 12/7 billion.
Less with a good accountant.

Originally posted by wolfgang59
They end up with 18/7 billion each.
IRS gets 12/7 billion.
Less with a good accountant.

Is that supposed to be 18.7 and 12.7 billion? Even if you say they end up with 7 billion each that is more than they started with, 12 billion total. 4 billion each not 28 billion.

Originally posted by sonhouse
Is that supposed to be 18.7 and 12.7 billion? Even if you say they end up with 7 billion each that is more than they started with, 12 billion total. 4 billion each not 28 billion.

Ah, I think your answer is 18/7ths billion, 2.57 billion each. Then the IRS gets 8.2857 billion.

How did you arrive at that answer?

Originally posted by sonhouse
Ah, I think your answer is 18/7ths billion, 2.57 billion each. Then the IRS gets 8.2857 billion.

How did you arrive at that answer?

Let x = the portion of money given to the inventor by each partner.

Let y = the original partners share

y = 4 - x (1)

Let z = the inventors share

z = 6/10*3*x (2) ( the inventors share is 60% of 3 times whatever each partner gives)

Solve:

y = z

4 - x = 6/10*3*x

4 = x + 6/10*3*x

4 = x( 1 + 6/10*3 )

4 = x( 10/10 + 18/10 )

4 = x ( 28/10 )

x = 40/28 = 10/7

Then each partners share is:

y = 4 - x

y = 4 - 10/7

y = 28/7 - 10 /7

y = 18/7 billion

And the IRS get the difference:

12 - 4*18/7 = 12/7 billion

It took me until seeing the nice tidy answer that wolfgang got to figure out the simple algebraic result.

The way that you have the problem statement worded suggested repeating the iterative approach that you started, which would leave some error until the exact fractional representation of 18/7 was reached in your sum.

Originally posted by joe shmo
Let x = the portion of money given to the inventor by each partner.

Let y = the original partners share

y = 4 - x (1)

Let z = the inventors share

z = 6/10*3*x (2) ( the inventors share is 60% of 3 times whatever each partner gives)

Solve:

y = z

4 - x = 6/10*3*x

4 = x + 6/10*3*x

4 = x( 1 + 6/10*3 )

4 = x( 10/10 + 18/10 )
...[text shortened]... ould leave some error until the exact fractional representation of 18/7 was reached in your sum.

What I am curious about is the 12/7 is 1.714 billion but if the inventor ends up with 2.57 billion, if they just gave him 2.57 the tax would only be 40% of that which comes out at 1. 028 odd billion. How did the government end up with that amount? The dude gets screwed it looks like since now he gets 2.57 and the blood thirsty IRS gets 1.7 which now comes out at 66% instead of 40% they normally claim for that amount of money transferred.

If they each gave enough to give him 2.57 in the first place wouldn't the tax now be only a bit over 1 billion so there would be 700 odd million to split amongst the four of them?

Originally posted by sonhouse
What I am curious about is the 12/7 is 1.714 billion but if the inventor ends up with 2.57 billion, if they just gave him 2.57 the tax would only be 40% of that which comes out at 1. 028 odd billion. How did the government end up with that amount? The dude gets screwed it looks like since now he gets 2.57 and the blood thirsty IRS gets 1.7 which now comes o ...[text shortened]... e only a bit over 1 billion so there would be 700 odd million to split amongst the four of them?

If you give me 40% of your money I will have 66.7% of what you have!

😀

Originally posted by wolfgang59
If you give me 40% of your money I will have 66.7% of what you have!

😀

But he didn't give 40% he gave 66% and he KEEPS 40.

Originally posted by sonhouse
What I am curious about is the 12/7 is 1.714 billion but if the inventor ends up with 2.57 billion, if they just gave him 2.57 the tax would only be 40% of that which comes out at 1. 028 odd billion. How did the government end up with that amount? The dude gets screwed it looks like since now he gets 2.57 and the blood thirsty IRS gets 1.7 which now comes o ...[text shortened]... e only a bit over 1 billion so there would be 700 odd million to split amongst the four of them?

if they just gave him 2.57 the tax would only be 40% of that which comes out at 1. 028 odd billion

Your a little backwards on this:

If the inventor after taxes has 2.57, then they would have needed to give him more than 2.57. explicitly:

let the amount the partners contribute = x

the amount the IRS takes = 0.4*x

This is equivalent to the following equation

x - 0.4*x = 2.57

If you solve for "x" ( the amount they need to contribute for the fourth partner to have 2.57 after the IRS takes 40😵 what do you get?

After you solve for "x" take the difference "y" ( this is the amount the IRS takes)

y = x - 2.57

What is the percentage the IRS has of the new partners share?

%IRS = y/2.57

Originally posted by sonhouse
But he didn't give 40% he gave 66% and he KEEPS 40.

No. He gave 40% of what he was given to IRS and kept 60%.

That 40% as a percentage of the 60% is 66.7%

Originally posted by wolfgang59
No. He gave 40% of what he was given to IRS and kept 60%.

That 40% as a percentage of the 60% is 66.7%

So the gist is you need to get 1.66 times the ending money to get that end money.

Originally posted by sonhouse
So the gist is you need to get 1.66 times the ending money to get that end money.

yep.

Death and taxes. The only certainties in life.

Originally posted by wolfgang59
yep.

Death and taxes. The only certainties in life.

And now the only thing we are sure of is taxes, considering the progress made in life extension🙂

Here is a step-by-step solution to the Mann-Mo-Jack problem:
-MMJ give Ed Keuritesla x dollars.
-Ed ends up with .6x dollars.
-IRS gets .4x dollars.
M,M, and J each get the same as Ed or .6x dollars each. Thus:
M,M, and J get a total of 1.8x dollars.
M,M, and J's share, plus Ed's share, plus the IRS share equals 12 billion dollars.
4(.6x) + .4x= $12,000,000,000
2.8x= 12,000,000,000
x=4,285,714,285.72
.4x, the IRS share = .4(4,285,714,285.72)
= $1,714,285,714.28
So, M,M, and J gave Ed:
====== $4,285,714,285.72=========
The IRS took 40% or: $1,714,285,714.28, leaving Ed with:
$4,285,714,285.72- $1,714,285,714.28
= $2,571,428,571.43**
**(Rounding the figures caused to one cent difference you may have noticed)

Each of the four nouveau riche entrepreneurs were left with:
$2,571,428,571.43

To check: 4(2,571,428,571.43)= 10,285,714,285.72-this is the total of M,M,J,and Ed.
Add in the IRS share:
10,285,714,285.72+ 1,714,285,714.28= 12,000,000,000.
Voilá.