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PAGE 5

The Inheritance

My grandfather told me of a dilemma, he had to help an unfortunate friend many years ago.  "It was during WWII (World War 2) when my friend found out that his wife was going to have a baby.  Unfortunately, my friend was called to duty before the baby was born. 

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He felt strongly about making out his will before he left, just in case.  He wanted his savings to be divided between his wife and his child to be.  If it were a boy, the child would get twice the amount of the mother.  If it were a girl, the child would get half the amount of the mother.  He had $14,000 in his savings account.

I do not begin to comprehend how he determined this strange will but this is what it was.  Even stranger still, my friends wife gave birth to twins... and yes, one was a boy and the other a girl?!? "

Before I tell you the answer what do you think? How was the money divided?
Answer: Mom gets $4,000; Son gets $8,000; Daughter gets $2,000.    Moms portion plus the son's double and the daughter's half portion equals 3.5. So: x + 2x + .5x = 3.5x and 3.5x = $14,000

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How Many Problems Did We Do???

I (Mr. T) assigned one homework problem for Monday night.  On each of the following nights for the rest of the week, I assigned three times as many problems as on the previous night.  At the end of the week, all the problems from the chapter had been assigned.  How many problems does the chapter have???

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Answer: The Chapter has 121 problems.   The assignmenst are 1 problem on Monday, 3 problems on Tuesday, 9 problems on Wednesday, 27 problems on Thursday, and 81 problems on Friday.   Add them up and get 121.

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A  Radio Contest

My friend Bob, has won a radio contest that includes a chance to win money.  A box is filled with $100, $50, $20, $10, and $5 bills.  Bob will be blindfolded and allowed to draw bills, one at a time, until he has drawn five bills of the same denomination.  What is the least amount of money that Bob can win? What is the most money he can win? EXPLAIN your answers for 2 points.

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Answer: The least is $25, although it is highly unlikely that it would occur.  He would have picked 5 $5 bills. The most he could win would be $840.  This is also unlikely but it would happen if he picked 4 of each bill then picked the $100 a last time to make 5 of them. 

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THE STORY OF 3 BROTHERS AND 17 CAMELS

In an arabic country, since there was no money, wealth was measured in real assets,like camels.

At that time, there was a wealthy men who had 3 sons. Among his most prized posessions were 17 camels. He was also known to be very shrewed. In his will, he determined that his oldest son should get of his estate ( = whatever he owned at the time of death), while his second born son should inherit 1/3 of his estate. His youngest son, being the yougest should inherit 1/9 of his estate. (In case you wonder, at that time people did not believe in fairneass. The first born son was always prefered). After the father died, the three brothers were quite happy to inherit that wealth. After all, owning 17 camels is like owning 17 big trucks today except that trucks do not produce milk while camels do. They loved and respected their father very much so they were quite eager to satisfy the will of their father exactly. However, they did not like the idea of killing some of the camels in order to honor the last will of their father:

of 17 camels makes 8 and of a camel figured the oldest brother, 1/3 of 17 camels makes 5 and 2/3 of a camel calculated the second brother, 1/9 of 17 canels makes only 1 and 8/9 camels thought the youngest brother. A dead camel was not worth much, so it made perfect sense that they hesitated to proceed with the execution of the will. How could have our father made such a mistake in his will, they thought. He must have been very bad in arithmetic they thought. They asked their friends for advice, but nobody really knew what to do in this case. Finally, somebody recommended that they travel to the next large city where a well known old philosopher was living. He was known to have solved many difficult problems. Eager to solve their problem, they followed that advice and travelled to the big city (taking their camels with them - you could not leave anything behind since there was no police at that time) and found the wise men after some effort.

The philosopher offered them some tea and then listened to their story. "I agree, this is a difficult problem and I do not know what to do. But please come back tomorrow morning, perhaps I have an idea over night".

The next morning they came back and found the old men already expecting them. Says he: "This was indeed a very difficult problem, and I had to think all the night long before I saw how to solve it. Before solving your problem, let me make you a gift. I am very much impressed by your eagerness to honor the will of your father, so I will give you in addition to the 17 camels you already own one more camel out of my own possession."

The three brothers were now very excited, they got a free camel, great! OK, said the old man. Let’s now try to execute the will of your father. You, the oldest son, how much are you supposed to get? One half of 18 camels, says the oldest son. That makes 9 camels concludes he with satisfaction in his voice. And you, second som, how much are you supposed to get? Well, answers he, one third. OK, how much is one third of 18 asks the philosopher? Sir, that’s 6 camels. OK take the 6 camels. Finally, he turns to the youngest son and asks him: How many camels do you get? Well sir, answers the third brother, I am supposed to get 1/9 of 18 camels which makes precisely 2 camels.

The three brothers take the 9 plus 6 plus 2 camels away and discover to their surprise that there is one camel left. (9+6+2 = 17 but there were 18 camels). "This camel", says the old man, "happens to be my own camel and, although I gave it to you as a present, I will now take it back as a fee for the service I performed by solving the problem".

The three brothers were extremely pleased. No camel had to be killed, and yet the will of their father was completely satified. Full of admiration for the wisdom of the old men, they thanked him many times and left back home. Going over the miraculous solutionm on the way home, they started to realize that their father must have known arithmetic much better than they thought originally.

Question: What is the mathematical explanation behind this miraculous solution? This is worth 5 points for the right explanation.

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Answer:  This has to do with Fractions:

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Becky's Phone Call

Becky wants to make a long distance call to her best freind Sarah from a pay telephone.  She has $5.00 in change.  The call costs $0.90 for the first three minutes and $0.24 for  each additional minute.  How long can Becky talk to Sarah? How much will she have left over? (Write an equation and solve it for one more point.) BS00864A.gif (2535 bytes)
 

Answer:   Twenty minutes.  After the first three minutes, Becky has $4.10 left.  At $0.24 per minute, she can talk for seventeen more (17 x 0.24 = $4.08) with $0.02 left over.

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This is a classic... Where's the Dollar?!?

Three guys in a hotel call room service and order two large pizzas. Thedelivery boy brings them up with a bill for exactly $30.00. Each guy gives him a $10.00 bill, and he leaves.

That’s fact!

When he hands the $30.00 to the cashier, he is told a mistake was made. The bill was only $25.00, not $30.00. The cashier gives the delivery boy five $1.00 bills and tells him to take it back to the 3 guys who ordered the pizza.

That’s fact!

On the way back to their room, the delivery boy has a thought... these guys did not give him a tip. He figures that since there is no way to split $5.00 evenly three ways anyhow, he will keep two dollars for himself and give them back three dollars.

OK! So far so good!

He knocks on the door and one fellow answers. He explains about a mix up in the bill, and hands he guy the three dollars, then departs with his two-dollar tip in his pocket.

Now the fun begins!

Remember $30-$25=$5 Right? $5-$3=$2 Right?

So what’s the problem? All is well, right? Not quite. Answer this: Each of the three guys originally gave $10.00 each.They each got back $1.00 in change. That means they paid $9.00 each, which times three is $27.00. The delivery boy kept $2.00 for a tip. $27.00 plus $2.00 equals $29.00. Where the heck is the other dollar ??????????

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Answer: The trick is to go back to the beginning.  There is no real problem here.  They only paid $27.   Don't be fooled by the question of where the other dollar is... it is there... look at the problem from this point of view...  They each paid $9 so they paid a total of $27.  $25 went for the pizza and $2 for the tip... done.  end of story.  The rest is just subterfuge.   (Look it up!)

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Another Calendar Question
     What is the smallest possible sum of the monthly calendar dates of two consecutive Wednesdays?   For example,  the first two Wednesdays of April 2000 fall on the 5th and 12th, so the sum of their dates is 5 + 12 = 17.  What is the greatest possible sum.   Take your time and think about these questions.  (2 points possible.)

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Answer: The smallest sum is 9, or 1 +  8The greatest sum is 55, or 24 + 31.   The greates sum occurs ony in 31 - day months.

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How Many Home Runs?
     After 108 games in 1999, Mark McGwire had accumulated 42 home runs.  At that point, what was his projected season-home-run total if 162 games are in the season?  For another point: how many home runs did he actually hit that year?

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Answer: 63 home runsMark hits 7 home runs in every 18 games.  Since there are 54 games left, and 54 18 is 3, then 3 x 7 is 21 more home runs in the remaining games. You could also set up a proportion: 42/108 = x /162.       x = 63

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Vacation Questions #2
Question #1: (3 pts)

)How many students?

Seventy-five students have just returned from a class trip to Washington, D.C.   The students visited the following sites:

Twenty students visited the Washington Monument
Thirty-five students visited the White House
Fifteen students visited the Kennedy Center
Ten students visited the White House and the kennedy Center
Eight students visited the Washington Monument and the White House
Six students visited the Washington Monument and the kennedy Center
Four students visited all three sites

How many students did not go to any of these sites? (Hint: use a vienne diagram.)

 

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Question #2 (2 pts)

How Many Apples in a Bag?

Five paper bags contain a total of thiry apples.   The first and the second contain a total of fourteen apples, the second and the third contain a total of ten apples, the third and fourth contain a total of nine apples, and the fourth and fifth contain a total of twelve apples.  How many apples are in each bag?

 

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Queston #3 (2 pts)

What's my Number?

Name a five digit number that meets the following requirements:

The first digit on the left tells how many times the digit 0 is in the number.
The second digit from the left tells how many times the digit 1 is in the number.
The third digit from the left tells how many times the digit 2 is in the number.
The fourth digit from the left tells how many times the digit 3 is in the number.
The fifth digit from the left tells how many times the digit 4 is in the number.

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Answers:

Question #1: 25 studentsUsing a Venn diagram is best here.   When adding all the numbers up there are only 50 students who visited the places.

Question #2: Bag1 = 8, bag2 = 6, bag3 = 4, bag4 = 5, bag5 = 7A helpful hint is that the bags have an average of 6 apples and then use trial and error.

Question #3: 21200Guess and check (trial and error) is the best method. 

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Page by: Mathman (Bruce A. Titen) 2000

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