Question 200849
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For each of them to have the same amount of money, they would each have to have a sum equal to the average of the three amounts.  The problem is to compute the difference between the amount of money they each have and that average amount.


Let *[tex \Large x] represent the amount Richard has.


Then Frank must have *[tex \Large x + 3] and George must have *[tex \Large x + 3 + 9 = x + 12]


The average of these three amounts is the sum of the amounts divided by 3:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x + x + 3 + x + 12}{3} = \frac{3x+15}{3} = x + 5]


In order for Richard who has *[tex \Large x] dollars to have *[tex \Large x + 5] dollars, he would have to <i>receive</i> 5 dollars.


In order for Frank who has *[tex \Large x + 3] dollars to have *[tex \Large x + 5] dollars, he would have to <i>receive</i> 2 dollars.


In order for George who has *[tex \Large x + 12] dollars to have *[tex \Large x + 5] dollars, he would have to <i>give</i> 7 dollars.


So George gives 2 dollars to Frank and 5 dollars to Richard.  Then George will have 7 dollars less and Frank will have 2 dollars more reducing their difference of 9 to zero.  And Frank will have 2 dollars more while Richard has 5 dollars more reducing their difference from 3 to zero.  Answer checks.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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