SOLUTION: George has 9 more dollars than Frank, who has 3 more than Richard. What is the least amount of money that must be exchanged so that they each have the same amount of money?

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Question 200849: George has 9 more dollars than Frank, who has 3 more than Richard. What is the least amount of money that must be exchanged so that they each have the same amount of money?
Answer by solver91311(24713) (Show Source):
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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 represent the amount Richard has.

Then Frank must have and George must have

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

In order for Richard who has dollars to have dollars, he would have to receive 5 dollars.

In order for Frank who has dollars to have dollars, he would have to receive 2 dollars.

In order for George who has dollars to have dollars, he would have to give 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