How to solve/what is the answer to the following word problem? Not homework/school work related!?

[lamarr3]

An older geocacher, being a GPSr horder, had tried to buy as many GPSr's as he could, but was finding himself well advanced in years. He called his boys together and told them that he wished to divide his GPSr’s between them while he was still alive. "Listen kid," he said to the eldest, "you may take as many Garmins as you think you could take care of, and your wife may have one ninth of all that are left."

Calling the second son he said, "Sport, you may take the same number of Garmin's that your older brother took, plus one extra Garmin because he had the first pick. To your wife, I will give one ninth of what will be left."

To the third son he made a similar statement. He was to take one Garmin more than the second son, and his wife was to have one ninth of those left. The same applied to the all other sons. Each took one Garmin more than his next oldest brother, and each son's wife took one ninth of the remainder.

After the youngest son had taken his share, there were none left for his wife. Then the old man said: "Since Delormes are worth more to some geocachers as Garmins, we will divide up my seven PN 60s so that each family will own property of equal value."

The problem is to tell how many Garmins the old man owned and how many did his daughters-in-law receive.


Once you know the total number of GPSr's, multiply that answer times six. Then, to that number, add the total number of GPSr's that his daughters-in law received. Lastly, add the number, 4 (four) to your result. You should have a three digit number to plug in. (A-B-C)

The Checksum of A+B+C = a two digit number, (D-E) and therefore D+E = 1

[wattekinson86]

Hi cncertluvr,

I'm going to guess that the Delormes are assumed to be Garmins, thus have the same value as Garmins.

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Then, assume the old man has 7 sons, and assume the eldest takes 2 Garmins, thus:

Total = 56; son takes 2, wife takes 6, son takes 3, wife takes 5, son takes 4, wife takes 4, son takes 5, wife takes 3, son takes 6, wife takes 2, son takes 7, wife takes 1, son takes 8.

So, each family gets 8 Garmins total.

Sharing 7 extra Garmins across the 7 families is easy; they get one each.

So, each family gets 9 Garmins.

Daughters-in-law received 6 + 5 + 4 + 3 + 2 + 1: 21 Garmins

The old man owned 56 in total, 56 * 6 + 21 + 4 = 361.
So, A = 3, B = 6, C = 1.
Thus A + B + C = 10.
So D = 1, E = 0.
Thus D + E = 1 as desired.

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Solution:
21 given to daughters-in-law.
56 owned by the old man in total.