Beautiful bride

Mister Lacky Jones was a rich married man. He had a son named Jay, and no other children.  When the son became 20 years old, he got married to a girl named Angel. Angel was really beautiful.  The bride and the groom started to live in the same house as Lacky and his wife.  After a few months, Lacky ‘s wife did not like Angel anymore.  Angel always tried to show that she was far more beautiful and quick witted than her mother in law. This rivalry resulted in frequent quarrels between the two. Jay’s mother and wife both complained to him almost on a daily basis.

Division of property

Lacky also warned Jay that if his wife kept this up, he would have to leave the house. Jay countered with a will from his grandfather showing a clause that gave him several rights to the property.  They wanted to go for a court battle but a counsellor convinced them to compromise.  It was decided that all the property should be divided into four equal parts – one would go to Lacky, another to his wife, a third to Jay and the fourth to Angel.  Lacky agreed to this settlement because he wanted his son to live well and did not want any court drama.  Also, he knew that upon the death of the parents, everything would belong to his son anyway. Other parties also agreed to the deal.

Lacky had  24,204 square meters of agricultural land, 32 cows, 9 houses and \$12,340,232 in cash in different accounts. The mediator assessed that all the agricultural land was of similar value.

Factors

Most of the decision was straight forward to divide each type of property in 4 parts.  For each item, he could divide the number with the factor 4.  When he factored the 24,204 square meters of land into 4, he got 6051 x 4. This meant that there were 4 equal lots of land of 6051 square meters each in the total land of 24,204 square meters. Cows were easy – because 32 could be factored into 8 x 4 meaning that each person would get 8 cows.

There were 9 houses. When he factored 9, he got 3 x 3.  There was no 4 in the factors. He examined the situation more carefully.  There were 8 houses of equal value.  He could divide them as 4 x 2, giving two houses to each person. The difficult part of the deal was the ninth small house.  He called a realtor and asked for its value.  The realtor said that this was a small house and needed a lot of repair but the value of the land in that area was very high.  Therefore, its price was about \$2,300,000.

Mediator’s suggestion

The mediator said that the small house (\$2,300,000) plus the cash (\$ 12,340,232) was worth \$14,640,232.  He factored this amount as 3,660,058 x 4.  He told them that they could either sell the house first or one of them could accept the house but take less cash.  The person who got this house would get \$2,300,000 less than the others.  Angel wanted to keep the house and others had no objection to it.  Lacky and his wife each received \$3,660,058 as did Jay but Angel got the house worth \$2,300,000 plus the cash amount of \$1,360,058.

Lacky thought that it to be good that the whole property had been divided into four parts to prevent future disputes.  The mediator could have given one half to Lacky and the other half to his son but then wives might have disputed this later on.

At the end, there was the matter of the fee for the mediator.  It had been agreed at \$50,000.  It was factored as \$12,500 x 4.  Each party paid \$12,500.

Challenge

Angel says that she has 9 jackets, 9 skirts, 16 shirts, 12 dresses and 18 pairs of shoes.  List the items whose numbers have 2 as a factor, 3 as a factor and both 2 and 3.

Solution:

Jackets: 9 = 3 x 3

Skirts: 9 = 3 x 3

Shirts: 16 = 2 x 2 x2 x 2

Dresses: 12 = 2 x 2 x 3

Shoes: 18 = 2 x 3 x 3.

Only the numbers of dresses and shoes  have 2 as a factor but the number of every item has 3 as a factor.

Supplementary

Sonia grew up in Delhi.  One day her friend Jaggu invited her to their family farm nearby.  Jaggu:  Our farm is 32 acres in area.  Our major crop is corn which we grow on half of the farm.  In the other half, we have three crops.  Half of this part is soybean,  and the other half is divided equally for potatoes and radish.   For us radish is a cash crop that gives us about 180,000 rupees per acre every year.

Sonia: So what does that work out to be for this cash crop per year for?

Jaggu drew this picture and said: Here is the 32 acre farm.  Half of this, meaning 16 acres, is for corn.  The other half is also 16  acres but half of this part which is 8 acres is for soybean leaving half of the 8 acres equally for potatoes and radish.  That means radish would be on half of the 8 acres which comes out to be 4 acres.  Now, at Rs. 180,000 per acre that is 4 x 180000 = 720,000 rupees.

Sonia: You could have also said that the radish is grown on 32 x (1/2) x (1/2) x (1/2) = 32 x (1/8) = 4 acres rather than talking about it the long way.