Hi,
I am having problems working out this percentage problem, which I'm
sure is really very simple.

Five partners receive shares in the following splits: 15%, 15%, 15%,
27.5%, 27.5%

The partnership wants to introduce a new partner and give him a share
that will be equal to the 15% guys new split.

All the existing partners must give a proportionately equal share of
their existing splits to accomodate the new partner.
What will be the new splits?

Hope you can help ..I'd love to see the method too if you don't mind

Thanks,
Jenny

"Jenny"  wrote in message 
news:drr913taa2u5sqjlhdl0h8a9g9dfpgn84n@4ax.com...
> Hi,
> I am having problems working out this percentage problem, which I'm
> sure is really very simple.
>
> Five partners receive shares in the following splits: 15%, 15%, 15%,
> 27.5%, 27.5%
>
> The partnership wants to introduce a new partner and give him a share
> that will be equal to the 15% guys new split.
>
> All the existing partners must give a proportionately equal share of
> their existing splits to accomodate the new partner.
> What will be the new splits?
>
> Hope you can help ..I'd love to see the method too if you don't mind
>

Add the 6th partner, giving 115% in total.  Then pro-rate all 6 
shareholdings down to 100 / 115ths.

BTW, accommodate has two "m"s :-)))


-- 
Martin

[Remove barrier to reply]

"Jenny"  wrote in message 
news:drr913taa2u5sqjlhdl0h8a9g9dfpgn84n@4ax.com...
> Hi,
> I am having problems working out this percentage problem, which I'm
> sure is really very simple.
>
> Five partners receive shares in the following splits: 15%, 15%, 15%,
> 27.5%, 27.5%
>
> The partnership wants to introduce a new partner and give him a share
> that will be equal to the 15% guys new split.
>
> All the existing partners must give a proportionately equal share of
> their existing splits to accomodate the new partner.
> What will be the new splits?
>
> Hope you can help ..I'd love to see the method too if you don't mind

Think in terms of a basic share and an enhanced share.

15% is a basic share,   27.5 is an enhanced share (enhancement is 11/6)

let y (in %)  be the new basic share, in the new arrangement the shares are:


y + y + y + y + 11y/6  + 11y/6    and that has to be = 100 (in %)

so 4y + 22y/6 = 100

solve for y

Brian

Thanks to you both ...and such speedy responses!

Jenny

Thu, 05 Apr 2007 13:58:15 +0100 from Jenny :
> Hi,
> I am having problems working out this percentage problem, which I'm
> sure is really very simple.
> 
> Five partners receive shares in the following splits: 15%, 15%, 15%,
> 27.5%, 27.5%

Hint: You have three folks with equal shares of X, and two folks with 
equal shares of 1.5X.

> The partnership wants to introduce a new partner and give him a share
> that will be equal to the 15% guys new split.

In other words, X.
 
> What will be the new splits?

Can you write an equation involving X?

-- 
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
                                  http://OakRoadSystems.com/

Thanks Stan ...except it's three folks with equal shares of X and two
with equal shares of 1.833_X  (not 1.5X)

Comes out X=13.04

Thanks,
Jenny



On Fri, 6 Apr 2007 01:18:04 -0400, Stan Brown
 wrote:

>Thu, 05 Apr 2007 13:58:15 +0100 from Jenny :
>> Hi,
>> I am having problems working out this percentage problem, which I'm
>> sure is really very simple.
>> 
>> Five partners receive shares in the following splits: 15%, 15%, 15%,
>> 27.5%, 27.5%
>
>Hint: You have three folks with equal shares of X, and two folks with 
>equal shares of 1.5X.
>
>> The partnership wants to introduce a new partner and give him a share
>> that will be equal to the 15% guys new split.
>
>In other words, X.
> 
>> What will be the new splits?
>
>Can you write an equation involving X?

[upside-down posting corrected; no extra charge :-) ]

Fri, 06 Apr 2007 12:15:12 +0100 from Jenny :
> On Fri, 6 Apr 2007 01:18:04 -0400, Stan Brown
>  wrote:
> 
> >Thu, 05 Apr 2007 13:58:15 +0100 from Jenny :
> >> Five partners receive shares in the following splits: 15%, 15%, 15%,
> >> 27.5%, 27.5%
> >
> >Hint: You have three folks with equal shares of X, and two folks with 
> >equal shares of 1.5X.
>
> Thanks Stan ...except it's three folks with equal shares of X and two
> with equal shares of 1.833_X  (not 1.5X)

You are 99% right -- and may I remark in passing that I love it when 
a student corrects me. I know of no better proof that the student now 
understands, which is the whole point of the exercise.

I say "99% right" because in fact the two shares are (11/6)X or 
11X/6, not 1.833X. You should always solve exactly when possible, and 
make a decimal approximation at the end, if at all.

> >> The partnership wants to introduce a new partner and give him a share
> >> that will be equal to the 15% guys new split.
> >
> >In other words, X.
> > 
> >> What will be the new splits?
> >
> >Can you write an equation involving X?

> Comes out X=13.04

That's an equation involving X, all right, :-) but I had in mind one  
more like
	4*X + 2*(11/6)*X = 1     <-- thanks to your correction

The solution:
	(4 + 11/3)X = 1
	(23/3)X = 1
	X = 3/23 = about .1304 or 13.04%

-- 
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
                                  http://OakRoadSystems.com/

"Jenny"  wrote in message 
news:drr913taa2u5sqjlhdl0h8a9g9dfpgn84n@4ax.com...
> Hi,
> I am having problems working out this percentage problem, which I'm
> sure is really very simple.
>
> Five partners receive shares in the following splits: 15%, 15%, 15%,
> 27.5%, 27.5%
>
> The partnership wants to introduce a new partner and give him a share
> that will be equal to the 15% guys new split.
>
> All the existing partners must give a proportionately equal share of
> their existing splits to accomodate the new partner.
> What will be the new splits?
>
> Hope you can help ..I'd love to see the method too if you don't mind
>

Add the 6th partner, giving 115% in total.  Then pro-rate all 6 
shareholdings down to 100 / 115ths.

BTW, accommodate has two "m"s :-)))


-- 
Martin

[Remove barrier to reply]

"Jenny"  wrote in message 
news:drr913taa2u5sqjlhdl0h8a9g9dfpgn84n@4ax.com...
> Hi,
> I am having problems working out this percentage problem, which I'm
> sure is really very simple.
>
> Five partners receive shares in the following splits: 15%, 15%, 15%,
> 27.5%, 27.5%
>
> The partnership wants to introduce a new partner and give him a share
> that will be equal to the 15% guys new split.
>
> All the existing partners must give a proportionately equal share of
> their existing splits to accomodate the new partner.
> What will be the new splits?
>
> Hope you can help ..I'd love to see the method too if you don't mind

Think in terms of a basic share and an enhanced share.

15% is a basic share,   27.5 is an enhanced share (enhancement is 11/6)

let y (in %)  be the new basic share, in the new arrangement the shares are:


y + y + y + y + 11y/6  + 11y/6    and that has to be = 100 (in %)

so 4y + 22y/6 = 100

solve for y

Brian

Thanks to you both ...and such speedy responses!

Jenny

Thu, 05 Apr 2007 13:58:15 +0100 from Jenny :
> Hi,
> I am having problems working out this percentage problem, which I'm
> sure is really very simple.
> 
> Five partners receive shares in the following splits: 15%, 15%, 15%,
> 27.5%, 27.5%

Hint: You have three folks with equal shares of X, and two folks with 
equal shares of 1.5X.

> The partnership wants to introduce a new partner and give him a share
> that will be equal to the 15% guys new split.

In other words, X.
 
> What will be the new splits?

Can you write an equation involving X?

-- 
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
                                  http://OakRoadSystems.com/

Thanks Stan ...except it's three folks with equal shares of X and two
with equal shares of 1.833_X  (not 1.5X)

Comes out X=13.04

Thanks,
Jenny



On Fri, 6 Apr 2007 01:18:04 -0400, Stan Brown
 wrote:

>Thu, 05 Apr 2007 13:58:15 +0100 from Jenny :
>> Hi,
>> I am having problems working out this percentage problem, which I'm
>> sure is really very simple.
>> 
>> Five partners receive shares in the following splits: 15%, 15%, 15%,
>> 27.5%, 27.5%
>
>Hint: You have three folks with equal shares of X, and two folks with 
>equal shares of 1.5X.
>
>> The partnership wants to introduce a new partner and give him a share
>> that will be equal to the 15% guys new split.
>
>In other words, X.
> 
>> What will be the new splits?
>
>Can you write an equation involving X?

[upside-down posting corrected; no extra charge :-) ]

Fri, 06 Apr 2007 12:15:12 +0100 from Jenny :
> On Fri, 6 Apr 2007 01:18:04 -0400, Stan Brown
>  wrote:
> 
> >Thu, 05 Apr 2007 13:58:15 +0100 from Jenny :
> >> Five partners receive shares in the following splits: 15%, 15%, 15%,
> >> 27.5%, 27.5%
> >
> >Hint: You have three folks with equal shares of X, and two folks with 
> >equal shares of 1.5X.
>
> Thanks Stan ...except it's three folks with equal shares of X and two
> with equal shares of 1.833_X  (not 1.5X)

You are 99% right -- and may I remark in passing that I love it when 
a student corrects me. I know of no better proof that the student now 
understands, which is the whole point of the exercise.

I say "99% right" because in fact the two shares are (11/6)X or 
11X/6, not 1.833X. You should always solve exactly when possible, and 
make a decimal approximation at the end, if at all.

> >> The partnership wants to introduce a new partner and give him a share
> >> that will be equal to the 15% guys new split.
> >
> >In other words, X.
> > 
> >> What will be the new splits?
> >
> >Can you write an equation involving X?

> Comes out X=13.04

That's an equation involving X, all right, :-) but I had in mind one  
more like
	4*X + 2*(11/6)*X = 1     <-- thanks to your correction

The solution:
	(4 + 11/3)X = 1
	(23/3)X = 1
	X = 3/23 = about .1304 or 13.04%

-- 
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
                                  http://OakRoadSystems.com/

"Jenny"  wrote in message 
news:drr913taa2u5sqjlhdl0h8a9g9dfpgn84n@4ax.com...
> Hi,
> I am having problems working out this percentage problem, which I'm
> sure is really very simple.
>
> Five partners receive shares in the following splits: 15%, 15%, 15%,
> 27.5%, 27.5%
>
> The partnership wants to introduce a new partner and give him a share
> that will be equal to the 15% guys new split.
>
> All the existing partners must give a proportionately equal share of
> their existing splits to accomodate the new partner.
> What will be the new splits?
>
> Hope you can help ..I'd love to see the method too if you don't mind
>

Add the 6th partner, giving 115% in total.  Then pro-rate all 6 
shareholdings down to 100 / 115ths.

BTW, accommodate has two "m"s :-)))


-- 
Martin

[Remove barrier to reply]

"Jenny"  wrote in message 
news:drr913taa2u5sqjlhdl0h8a9g9dfpgn84n@4ax.com...
> Hi,
> I am having problems working out this percentage problem, which I'm
> sure is really very simple.
>
> Five partners receive shares in the following splits: 15%, 15%, 15%,
> 27.5%, 27.5%
>
> The partnership wants to introduce a new partner and give him a share
> that will be equal to the 15% guys new split.
>
> All the existing partners must give a proportionately equal share of
> their existing splits to accomodate the new partner.
> What will be the new splits?
>
> Hope you can help ..I'd love to see the method too if you don't mind

Think in terms of a basic share and an enhanced share.

15% is a basic share,   27.5 is an enhanced share (enhancement is 11/6)

let y (in %)  be the new basic share, in the new arrangement the shares are:


y + y + y + y + 11y/6  + 11y/6    and that has to be = 100 (in %)

so 4y + 22y/6 = 100

solve for y

Brian

Thanks to you both ...and such speedy responses!

Jenny

Thu, 05 Apr 2007 13:58:15 +0100 from Jenny :
> Hi,
> I am having problems working out this percentage problem, which I'm
> sure is really very simple.
> 
> Five partners receive shares in the following splits: 15%, 15%, 15%,
> 27.5%, 27.5%

Hint: You have three folks with equal shares of X, and two folks with 
equal shares of 1.5X.

> The partnership wants to introduce a new partner and give him a share
> that will be equal to the 15% guys new split.

In other words, X.
 
> What will be the new splits?

Can you write an equation involving X?

-- 
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
                                  http://OakRoadSystems.com/

Thanks Stan ...except it's three folks with equal shares of X and two
with equal shares of 1.833_X  (not 1.5X)

Comes out X=13.04

Thanks,
Jenny



On Fri, 6 Apr 2007 01:18:04 -0400, Stan Brown
 wrote:

>Thu, 05 Apr 2007 13:58:15 +0100 from Jenny :
>> Hi,
>> I am having problems working out this percentage problem, which I'm
>> sure is really very simple.
>> 
>> Five partners receive shares in the following splits: 15%, 15%, 15%,
>> 27.5%, 27.5%
>
>Hint: You have three folks with equal shares of X, and two folks with 
>equal shares of 1.5X.
>
>> The partnership wants to introduce a new partner and give him a share
>> that will be equal to the 15% guys new split.
>
>In other words, X.
> 
>> What will be the new splits?
>
>Can you write an equation involving X?

[upside-down posting corrected; no extra charge :-) ]

Fri, 06 Apr 2007 12:15:12 +0100 from Jenny :
> On Fri, 6 Apr 2007 01:18:04 -0400, Stan Brown
>  wrote:
> 
> >Thu, 05 Apr 2007 13:58:15 +0100 from Jenny :
> >> Five partners receive shares in the following splits: 15%, 15%, 15%,
> >> 27.5%, 27.5%
> >
> >Hint: You have three folks with equal shares of X, and two folks with 
> >equal shares of 1.5X.
>
> Thanks Stan ...except it's three folks with equal shares of X and two
> with equal shares of 1.833_X  (not 1.5X)

You are 99% right -- and may I remark in passing that I love it when 
a student corrects me. I know of no better proof that the student now 
understands, which is the whole point of the exercise.

I say "99% right" because in fact the two shares are (11/6)X or 
11X/6, not 1.833X. You should always solve exactly when possible, and 
make a decimal approximation at the end, if at all.

> >> The partnership wants to introduce a new partner and give him a share
> >> that will be equal to the 15% guys new split.
> >
> >In other words, X.
> > 
> >> What will be the new splits?
> >
> >Can you write an equation involving X?

> Comes out X=13.04

That's an equation involving X, all right, :-) but I had in mind one  
more like
	4*X + 2*(11/6)*X = 1     <-- thanks to your correction

The solution:
	(4 + 11/3)X = 1
	(23/3)X = 1
	X = 3/23 = about .1304 or 13.04%

-- 
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
                                  http://OakRoadSystems.com/

"Jenny"  wrote in message 
news:drr913taa2u5sqjlhdl0h8a9g9dfpgn84n@4ax.com...
> Hi,
> I am having problems working out this percentage problem, which I'm
> sure is really very simple.
>
> Five partners receive shares in the following splits: 15%, 15%, 15%,
> 27.5%, 27.5%
>
> The partnership wants to introduce a new partner and give him a share
> that will be equal to the 15% guys new split.
>
> All the existing partners must give a proportionately equal share of
> their existing splits to accomodate the new partner.
> What will be the new splits?
>
> Hope you can help ..I'd love to see the method too if you don't mind
>

Add the 6th partner, giving 115% in total.  Then pro-rate all 6 
shareholdings down to 100 / 115ths.

BTW, accommodate has two "m"s :-)))


-- 
Martin

[Remove barrier to reply]

"Jenny"  wrote in message 
news:drr913taa2u5sqjlhdl0h8a9g9dfpgn84n@4ax.com...
> Hi,
> I am having problems working out this percentage problem, which I'm
> sure is really very simple.
>
> Five partners receive shares in the following splits: 15%, 15%, 15%,
> 27.5%, 27.5%
>
> The partnership wants to introduce a new partner and give him a share
> that will be equal to the 15% guys new split.
>
> All the existing partners must give a proportionately equal share of
> their existing splits to accomodate the new partner.
> What will be the new splits?
>
> Hope you can help ..I'd love to see the method too if you don't mind

Think in terms of a basic share and an enhanced share.

15% is a basic share,   27.5 is an enhanced share (enhancement is 11/6)

let y (in %)  be the new basic share, in the new arrangement the shares are:


y + y + y + y + 11y/6  + 11y/6    and that has to be = 100 (in %)

so 4y + 22y/6 = 100

solve for y

Brian

Thanks to you both ...and such speedy responses!

Jenny

Thu, 05 Apr 2007 13:58:15 +0100 from Jenny :
> Hi,
> I am having problems working out this percentage problem, which I'm
> sure is really very simple.
> 
> Five partners receive shares in the following splits: 15%, 15%, 15%,
> 27.5%, 27.5%

Hint: You have three folks with equal shares of X, and two folks with 
equal shares of 1.5X.

> The partnership wants to introduce a new partner and give him a share
> that will be equal to the 15% guys new split.

In other words, X.
 
> What will be the new splits?

Can you write an equation involving X?

-- 
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
                                  http://OakRoadSystems.com/

Thanks Stan ...except it's three folks with equal shares of X and two
with equal shares of 1.833_X  (not 1.5X)

Comes out X=13.04

Thanks,
Jenny



On Fri, 6 Apr 2007 01:18:04 -0400, Stan Brown
 wrote:

>Thu, 05 Apr 2007 13:58:15 +0100 from Jenny :
>> Hi,
>> I am having problems working out this percentage problem, which I'm
>> sure is really very simple.
>> 
>> Five partners receive shares in the following splits: 15%, 15%, 15%,
>> 27.5%, 27.5%
>
>Hint: You have three folks with equal shares of X, and two folks with 
>equal shares of 1.5X.
>
>> The partnership wants to introduce a new partner and give him a share
>> that will be equal to the 15% guys new split.
>
>In other words, X.
> 
>> What will be the new splits?
>
>Can you write an equation involving X?

[upside-down posting corrected; no extra charge :-) ]

Fri, 06 Apr 2007 12:15:12 +0100 from Jenny :
> On Fri, 6 Apr 2007 01:18:04 -0400, Stan Brown
>  wrote:
> 
> >Thu, 05 Apr 2007 13:58:15 +0100 from Jenny :
> >> Five partners receive shares in the following splits: 15%, 15%, 15%,
> >> 27.5%, 27.5%
> >
> >Hint: You have three folks with equal shares of X, and two folks with 
> >equal shares of 1.5X.
>
> Thanks Stan ...except it's three folks with equal shares of X and two
> with equal shares of 1.833_X  (not 1.5X)

You are 99% right -- and may I remark in passing that I love it when 
a student corrects me. I know of no better proof that the student now 
understands, which is the whole point of the exercise.

I say "99% right" because in fact the two shares are (11/6)X or 
11X/6, not 1.833X. You should always solve exactly when possible, and 
make a decimal approximation at the end, if at all.

> >> The partnership wants to introduce a new partner and give him a share
> >> that will be equal to the 15% guys new split.
> >
> >In other words, X.
> > 
> >> What will be the new splits?
> >
> >Can you write an equation involving X?

> Comes out X=13.04

That's an equation involving X, all right, :-) but I had in mind one  
more like
	4*X + 2*(11/6)*X = 1     <-- thanks to your correction

The solution:
	(4 + 11/3)X = 1
	(23/3)X = 1
	X = 3/23 = about .1304 or 13.04%

-- 
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
                                  http://OakRoadSystems.com/

"Jenny"  wrote in message 
news:drr913taa2u5sqjlhdl0h8a9g9dfpgn84n@4ax.com...
> Hi,
> I am having problems working out this percentage problem, which I'm
> sure is really very simple.
>
> Five partners receive shares in the following splits: 15%, 15%, 15%,
> 27.5%, 27.5%
>
> The partnership wants to introduce a new partner and give him a share
> that will be equal to the 15% guys new split.
>
> All the existing partners must give a proportionately equal share of
> their existing splits to accomodate the new partner.
> What will be the new splits?
>
> Hope you can help ..I'd love to see the method too if you don't mind
>

Add the 6th partner, giving 115% in total.  Then pro-rate all 6 
shareholdings down to 100 / 115ths.

BTW, accommodate has two "m"s :-)))


-- 
Martin

[Remove barrier to reply]

"Jenny"  wrote in message 
news:drr913taa2u5sqjlhdl0h8a9g9dfpgn84n@4ax.com...
> Hi,
> I am having problems working out this percentage problem, which I'm
> sure is really very simple.
>
> Five partners receive shares in the following splits: 15%, 15%, 15%,
> 27.5%, 27.5%
>
> The partnership wants to introduce a new partner and give him a share
> that will be equal to the 15% guys new split.
>
> All the existing partners must give a proportionately equal share of
> their existing splits to accomodate the new partner.
> What will be the new splits?
>
> Hope you can help ..I'd love to see the method too if you don't mind

Think in terms of a basic share and an enhanced share.

15% is a basic share,   27.5 is an enhanced share (enhancement is 11/6)

let y (in %)  be the new basic share, in the new arrangement the shares are:


y + y + y + y + 11y/6  + 11y/6    and that has to be = 100 (in %)

so 4y + 22y/6 = 100

solve for y

Brian

Thanks to you both ...and such speedy responses!

Jenny

Thu, 05 Apr 2007 13:58:15 +0100 from Jenny :
> Hi,
> I am having problems working out this percentage problem, which I'm
> sure is really very simple.
> 
> Five partners receive shares in the following splits: 15%, 15%, 15%,
> 27.5%, 27.5%

Hint: You have three folks with equal shares of X, and two folks with 
equal shares of 1.5X.

> The partnership wants to introduce a new partner and give him a share
> that will be equal to the 15% guys new split.

In other words, X.
 
> What will be the new splits?

Can you write an equation involving X?

-- 
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
                                  http://OakRoadSystems.com/

Thanks Stan ...except it's three folks with equal shares of X and two
with equal shares of 1.833_X  (not 1.5X)

Comes out X=13.04

Thanks,
Jenny



On Fri, 6 Apr 2007 01:18:04 -0400, Stan Brown
 wrote:

>Thu, 05 Apr 2007 13:58:15 +0100 from Jenny :
>> Hi,
>> I am having problems working out this percentage problem, which I'm
>> sure is really very simple.
>> 
>> Five partners receive shares in the following splits: 15%, 15%, 15%,
>> 27.5%, 27.5%
>
>Hint: You have three folks with equal shares of X, and two folks with 
>equal shares of 1.5X.
>
>> The partnership wants to introduce a new partner and give him a share
>> that will be equal to the 15% guys new split.
>
>In other words, X.
> 
>> What will be the new splits?
>
>Can you write an equation involving X?

[upside-down posting corrected; no extra charge :-) ]

Fri, 06 Apr 2007 12:15:12 +0100 from Jenny :
> On Fri, 6 Apr 2007 01:18:04 -0400, Stan Brown
>  wrote:
> 
> >Thu, 05 Apr 2007 13:58:15 +0100 from Jenny :
> >> Five partners receive shares in the following splits: 15%, 15%, 15%,
> >> 27.5%, 27.5%
> >
> >Hint: You have three folks with equal shares of X, and two folks with 
> >equal shares of 1.5X.
>
> Thanks Stan ...except it's three folks with equal shares of X and two
> with equal shares of 1.833_X  (not 1.5X)

You are 99% right -- and may I remark in passing that I love it when 
a student corrects me. I know of no better proof that the student now 
understands, which is the whole point of the exercise.

I say "99% right" because in fact the two shares are (11/6)X or 
11X/6, not 1.833X. You should always solve exactly when possible, and 
make a decimal approximation at the end, if at all.

> >> The partnership wants to introduce a new partner and give him a share
> >> that will be equal to the 15% guys new split.
> >
> >In other words, X.
> > 
> >> What will be the new splits?
> >
> >Can you write an equation involving X?

> Comes out X=13.04

That's an equation involving X, all right, :-) but I had in mind one  
more like
	4*X + 2*(11/6)*X = 1     <-- thanks to your correction

The solution:
	(4 + 11/3)X = 1
	(23/3)X = 1
	X = 3/23 = about .1304 or 13.04%

-- 
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
                                  http://OakRoadSystems.com/