Adjusted winner procedure...the final step Pease Help!

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cruz33

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I please need help with the final part of this problem:

This is the problem:

Adjusted winner

(1) Each party distributes 100 points

Issue ........... Labor .. Management
Base salary ....... 30 .... 50
Salary increases .. 20 .... 40
Benefits .......... 35 ..... 5
Vacation time ..... 15 ..... 5

(2) Give item to the party with more points


Labor gets :
Benefits .......... 35
Vacation time ..... 15
Total ............. 50

Management gets:
Base salary ....... 50
Salary increases .. 40
Total ............. 90

I have calculated that far but then I have to calculate thewinner's point value for the item and the loser's point value for the item. Howdo I calculate the winner's point value for the item and the loser's pointvalue for the item? This is the clue:
Transfer (fractional a part of) items in order of increasingpoint ratio.
And here is the link explaining how to do this: (but I stilldon’t get it)
http://www.math.wisc.edu/~meyer/math141/fairdivision1.html
 
Step 4 on your referenced page says, "go through the items on the winner's list and compute the point ratio".

It defines the point ratio (for each item) as the winner's point value divided by the loser's point value.

With 90 total points, management is the winner. They won the items 'base salary' and 'salary increases'.

So, those are the two items for which you need to calculate the point ratio.

Can you do that part now? Then, we continue to the system of equations...
 
So,
Salary increases ... 40 ÷ 20 = 2

Base salary ... 50 ÷ 20 = 2.5


Now what? How to I answer this question - How much is eachside keeping or giving up?

Thank you so far!


 
cruz33 said:

Salary increases ... 40 ÷ 20 = 2

Base salary ... 50 ÷ 20 = 2.5 This is not correct; please double-check your work.

Now what? How to I answer this question

We're working on it... :cool:
Click to expand...

I'm following the instructions in step 4, of the page that you referenced:

Transfer (fractional a part of) items in order of increasing point ratio.

We need to know the correct point-ratio values, before we can determine the increasing order. You need to correct the value 2.5 above.

Once you have the correct values, we will continue to the system of equations...
 
(winner'spoint value for the item) / (loser's point value for the item) Winner’s point value for item “base salary” is 50
Loser’s point value for this same item is 30
So, 50 ÷ 30 = 1.6666666666666667

O_O

 
Yes, you now have the correct point ratios.

Base Salary 1.7

Salary Increases 2

With these values, we see that the Base-Salary point-ratio is actually lower, not higher.

This means that Base Salary is the item for which the winner's points will be reduced by a percent. The loser's points for Base Salary will be increased by the same percent.

So, what's the percent? We want to choose the fractional amount that will cause the winner's and loser's point totals to equal.

Before the adjustment, the winner's points total 40 + 50, and the loser's points total 15 + 35

Let x = the unknown percent

The winner's points for Base Salary are 50, so the percentage 50x will be subtracted from their total.

40 + 50 - 50x

The loser's points for Base Salary are 20, so the percentage 20x will be added to their total.

15 + 35 + 20x

To be fair, the adjusted point totals must be equal, so that's where the equation comes from.

40 + 50 - 50x = 15 + 35 + 20x

Solve for x.


(I'm not sure why I was thinking about a system of equations, earlier. It's just one equation.)
 
Last edited:
X=4/7?
x=40/70?
0.57= x?


Not sure which one is the correct answer…
 
Yes, those are all the same number (the decimal form 0.57 is rounded, of course).

(Do not interchange symbols X and x. They are not the same symbol.)

So, the winner lost 57% of their points for Base Salary, and the loser's points for that item increased by 57%.

The adjusted point totals for Management and Labor are now equal.

What is this new point total?
 
So, the winner lost 57% of their points for Base Salary, and the loser's points for that item increased by 57%.

The adjusted point totals for Management and Labor are now equal.

What is this new point total?[/QUOTE]

Point total? Do I have to sum 57% plus 57%? Still don't understand who gets what? What each side is keeping or giving up? (I'm really bad at numbers, you can tell right?)
 
cruz33 said:
Point total? Do I have to sum 57% plus 57%?
Click to expand...

Let's round to four places, to avoid rounding error.

x = 0.5714



The adjusted point total for Management is 40 + 50 - 50x

The adjusted point total for Labor is 35 + 15 + 20x

Still don't understand who gets what? What each side is keeping or giving up?
Click to expand...

Management gets 40 points for Salary Increases and 50-50x points for Base Salary.

Labor gets 35 points for Benefits, 15 points for Vacations, and 20x points for Base Salary.

Do the arithmetic. :cool:
 
Management gets 40 points for Salary Increases and 50-50x points for Base Salary.

Labor gets 35 points for Benefits, 15 points for Vacations, and 20x points for Base Salary.

Do the arithmetic. :cool:[/QUOTE]

Sorry, you lost me with the “50-50x and the 20x” What else I need to do in order to get to the final answer? Honestly, I appreciate your patience with me!
 
Last edited:
Please excuse me. You solved the earlier equation, so I was thinking that you understood the remaining algebra.

The expression 50x represents the product 50 times x

We found that x=0.5714

Hence, the expression 50x means 50 times 0.5714

Use a calculator, to find this amount

Management's point total is 40 + 50 - 50x

Simply multiply 50 times 0.5714, and then subtract that amount from 90.



NOTE: On the reference page, they factored their expression.

In other words, written like that page, 40+50-50x would appear as 40+50(1-x)

Both expressions are the same.



Likewise, Labor's points are 35+15+20x, so you need to multiply 20 times 0.5714 and add the result to 50.



You ought to find that Management's points and Labor's points are now the same. And that's the whole point! :D
 
By the way, what did they ask for, in this exercise?

Do they want the adjusted point total?

Did they ask you for an itemized list of points?

Can you finish it?
 
So,
Management gets 40 points for Salary Increases and 50-50xpoints for Base Salary.

50 times 0.5714 = 28.57

28.57 – 90 = 19.57

Labor gets 35 points for Benefits, 15 points for Vacations, and 20x points forBase Salary.


20times + 0.5714 = 11.428

11.428+ 50 = 61.428

I probably did it wrong...right? I'm telling you, I'm terrible at numbers! Ha-ha I really appreciate your patience! According to the instruction I have to "Resolve this dispute"
 
Last edited:
cruz33 said:

50 times 0.5714 = 28.57

28.57 – 90 = 19.57 Subtracting 90 points is not correct.



Labor gets

11.428+ 50 = 61.428 :) Correct

I have to "Resolve this dispute"
Click to expand...

Yes, 50x is 28.57 -- that's how many points management loses in Base Salary

But, subtracting these points from 90 looks like this:

90 - 28.57 = 61.43

We see that 61.43 is the point total for both management and labor.

You have resolved the dispute.

Management won Salary Increases, and Labor won Benefits and Vacation Time.

Management and Labor must compromise on Base Salary, with management having about twice as many points in that negotiation (21.43 points versus 11.43 points).
 
Thank you thank you thank you

God bless your mind for being so smart!!! Thank you!!!!!!!!!!!!!!!!!! for your help and patience!!!!!!!!!!!!!:D:D:D
 
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