Word problems, kind of brain teasers

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JSG31883

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Sep 14, 2005
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I was reading a paper today and came across these two word problems and was unable to solve them. I don't know if they are solvable or not, but any help or thoughts would put my mind at ease. Thanks!

1) The product of the length of a boat, the age of the captain, and the number of his children is 32118. The captain has both sons and daughters. His age (as a number) is larger than the number of his children, and he is not yet 100 year olds. How old is he? How many children does he have? How long is his boat?

2) In preparation for Halloween, three married couples, the Browns, the Joneses, and the Smiths, bought treats for the children. Each bought as many identical presents as he or she paid cents for one of them. Each wife spent 75 cents more than her husband. Ann bought one more present than Bill Brown. Betty bought one less than Joe Jones. What is Mary's last name?
 
JSG31883 said:
1) The product of the length of a boat, the age of the captain, and the number of his children is 32118. The captain has both sons and daughters. His age (as a number) is larger than the number of his children, and he is not yet 100 year olds. How old is he? How many children does he have? How long is his boat?
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The captain is 53 years old, he has 6 children, and the length of his boat is 101 units.
 
What's the point of multi-posting? Don't waste other people's time!
 
But if you can't help me, then maybe someone else can... it's called being resourceful!
 
JSG31883 said:
But if you can't help me, then maybe someone else can... it's called being resourceful!
Click to expand...
But when the same people volunteer at the various different sites, it's called "multi-posting", and makes those volunteers less likely to answer, since, hey, somebody surely will answer somewhere else. Which is why it is generally recommended against, especially if you've not done any work of your own.

(Of course, what you've done isn't as bad as those who take the hints and suggestions they're given on one site, post it as their own work to a second site, take the help they get with the next step at that site, post that to a third site as their own work, etc, etc, snookering the tutors on various sites into doing their entire assignment for them. But the tutors do eventually figure it out....)

Eliz.
 
Sorry, I had no idea...

I have actually done some more work on the problem and since I'm training to be a teacher, have come up with a good way to approach the problem. Since we need to find the numbers whose product is 32118, we can break it down into its prime factorization.

32118= 2*16059
16059= 3*5353
5353= 53*101

We know the captains age can't be 101, so it must be either 6 or 53. But considering he has children and the number of children he has is smaller than his age, his age must be 53. Then he can either have 101, or 6 children, obviously making him have 6 children, and the length of the boat being 101.



I AM STILL STUCK, HOWEVER, ON THE SECOND PROBLEM... :(
 
JSG31883 said:
We know the captains age can't be 101, so it must be either 6 or 53.
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No, the captain's age is possibly either 2, 3, 53, or the product of any two or three of these numbers. A full solution to this problem would explain, for example, why the captain's age can't be 3.
 
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