SOLUTION: After Mr. Klopstock's death, it was found out that his state consisted of seventeen horses. His will provided that his friend Mr. Thom should be his executor. The terms of the will

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: After Mr. Klopstock's death, it was found out that his state consisted of seventeen horses. His will provided that his friend Mr. Thom should be his executor. The terms of the will      Log On


   

Question 1080847: After Mr. Klopstock's death, it was found out that his state consisted of seventeen horses. His will provided that his friend Mr. Thom should be his executor. The terms of the will were these:
1. One half of the horses should go to the widow;
2. One third to the elder son; and
3. One ninth of the horses to the younger son.
Mr. Thom was in great trouble. It was evident that drawing up his will, Mr. Klopstock had miscalculated. It would be impossible for any of the persons to receive a fraction of a horse. Yet, Mr. Thom solved the problem. How was it done?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i believe he may have done something like the following.

he added up the fractions as follows:

he determined the value of x that would make the fractions come out whole in the following manner.

1/2 * x + 1/3 * + 1/9 * x = 17

factor out the x and you get x * (1/2 + 1/3 + 1/9) = 17

place all the fractions under a common denominator to get:

x * (9/18 + 6/18 + 2/18) = 17

combine like terms to get x * 17/18 = 17

multiply both sides of this equation by 18/17 to get:

x = 17 * 18/17

solve for x to get x = 18.

he used x as the common denominator.

the widow gets 1/2 of 18 = 9

the elder son gets 1/3 of 18 = 6

the younger son gets 1/9 of 18 = 2

9 + 6 + 2 = 17

everybody gets a whole horse.

he could also have rounded the answers to the nearest whole number and would have gotten the same numbers.

17/2 = 8.5 = 9

17/3 = 5.7 = 6

17/9 = 1.9 = 2

9 + 6 + 2 = 17








Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
.
This problem is the old-fashioned (2000-3000 years old) entertainment problem.
The legend says, the solution is this: 

Mr. Thom added his own horse to 17 horses of the late/deceased Mr. Klopstock.

Then he divided the 18 = 17+1 horses in this way:

1/2 of 18 = 9 to the widow;

1/3 of 18 = 6 to the elder son;

1/9 of 18 = 2 to the younger son.


9 + 6 + 2 = 17,   and  18-17 = 1.


After completing his mission, Thom got on his horse and went home.


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The hidden meaning of this story is that   1%2F2+%2B+1%2F3+%2B+1%2F9 = 9%2F18+%2B+6%2F18+%2B+2%2F18 = %289%2B6%2B2%29%2F18 = 17%2F18  and is not  1  (one).