Question

A farmer died and left 17 cows to be divided among three workers. The first worker was to receive 1/2 of the cows, the second worker was to receive 1/3 of the cows, and the third worker was to receive 1/9 of the cows. The executor of the farmer's estate realized that 17 cows could not be divided into halves, thirds, or ninths, so they added a neighbor's cow to the farmer's. With 18 cows, the executor gave 9 cows to the first worker, 6 cows to the second worker, and 2 cows to the third worker. This accounted for the 17 cows, so the executor returned the borrowed cow to the neighbor. This solution works because by adding an extra cow, the total number of cows becomes divisible by 2, 3, and 9, allowing for a fair distribution among the three workers.

Answer 1

The executor of a farmer's estate creatively resolved the problem of dividing 17 cows among three workers in specific fractions by borrowing a neighbor's cow to make the count 18, allowing for an equitable division. Upon completing the division as 1/2, 1/3, and 1/9, 17 cows were distributed and the extra cow was returned.

Step-by-step explanation:

The problem presented is a classic example of dividing an inheritance among heirs that cannot be easily split into fractional parts due to indivisible items, in this case, cows. A farmer who owned 17 cows passed away, and his will instructed to divide the cows among three workers in fractional parts: 1/2 to the first, 1/3 to the second, and 1/9 to the third. To solve this, the executor used a creative solution by temporarily borrowing a neighbor's cow to make the total divisible by the fractions mentioned.

With 18 cows, the executor was able to distribute 9 cows (1/2) to the first worker, 6 cows (1/3) to the second, and 2 cows (1/9) to the third. Remarkably, this summed up to 17 cows, and the borrowed cow was returned, effectively resolving the issue while honoring the farmer's wishes. This method works due to the divisibility and compatibility of the chosen fractions with the number 18, which is divisible by 2, 3, and 9.

Fractions, division, and inheritance are crucial mathematical topics covered in this question. The executor's ingenuity demonstrates a practical application of mathematical concepts to resolve real-world problems. This example serves as an exercise in logic and division of assets, a skill useful in various fields involving mathematics and finance.