PEARLS FOR GIRLS

Once an old man died, and in his will he stated that all the pearls he kept in a little bag were to be distributed among his daughters. To make things fair, the distribution must be done in the following way:

The older girl should receive one pearl, and a seventh of the remaining pearls in the bag.

The second girl should receive two pearls, and a seventh of the remaining pearls in the bag.

The third girl should receive three pearls, and a seventh of the remaining pearls in the bag.

And so on until all the pearls are exhausted.

Needless to say, the younger girl grew angry, and went to talk to the Judge because, if distributed that way, she probably would not get a pearl at all.

The wise Judge looked at her and said: "Don't worry, my child. Your father was a wise man. He made everything quite right so that, after all the pearls are given, each one of you will have the same quantity of pearls and there will be no pearls left."

And so it was.

How many pearls were there in the bag?

How many daughters did the old man have?

How many pearls did each girl get?

Answer: 36 pearls, 6 daughters, 6 pearls for each daughter

MONKEY MADNESS

Three types of monkeys - monkeys of the same type weigh the same - were amusing themselves in the jungle. By chance they found a small wobbly tree, where, by varying the amounts of monkeys on each side they could keep the tree in an upright position.

They found out that:

2 howler monkeys and 1 squirrel monkey on one side balanced with 4 spider monkeys on the other side.

2 spider monkeys and 1 squirrel monkey on one side balanced with 3 howler monkeys on the other side.

Can you determine how many squirrel monkeys on one side it would take to keep the tree upright with 4 howler monkeys on the other side?

Answer: 3 squirrel monkeys

In the following explanation assume:

spider monkey =sp
squirrel monkey = sq
howler monkey = h

According to the first statement:
2h + 1sq = 4sp

Divide both sides by 2, giving:
1h + 1/2sq = 2sp

So, 2 spider monkeys equal 1 howler and half a squirrel.

Write an equation using the second statement:
2sp + 1sq = 3h

Now, substitute in 1h and 1/2sq for 2sp:
1h + 1/2sq + 1sq = 3h

Combine like terms:
1h + 1 ½sq = 3h

1 ½ sq = 2h

Double both sides of the equation:
3sq = 4h