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Alex111 science forum beginner
Joined: 08 Feb 2006
Posts: 17

Posted: Wed Jul 12, 2006 9:05 pm Post subject:
Word Problems



Hello! I would just like some answers and information to these topics. I really need help. And any information would be accepted. Please help me in the following:
1. Anne leaves town A traveling by bike to town B along a certain path at sunrise. Bart leaves town B travelling by bike to town A along the same path as Anne. They travel at a constant speed, and do not stop biking towards their final destinations. The cross each other's paths at noon. Anne gets to town B at 5:00pm and Bart gets to town A at 11:15pm. At what time was sunrise?
2. Show that there is no perfect square whose digits sum of to 2006. (7 points)
3. Two natural numbers, x and y, are taken such that their sum is less than 100. (x + y < 100) Both x and y are greater than 1. Sam is told the sum of the numbers (x + y) and Pam is told the product of the numbers (xy). Neither of them knows the original two numbers, x and y. They have the following conversation:
Pam: I cannot determine the sum of the numbers.
Sam: I know.
Pam: Now, I know their sum.
Sam: Now, I know their product.
Determine x and y.
PLEASE help me with whatever you can! Thank you! 

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Dave L. Renfro science forum Guru
Joined: 29 Apr 2005
Posts: 570

Posted: Wed Jul 12, 2006 10:42 pm Post subject:
Re: Word Problems



Alex wrote:
Quote:  Hello! I would just like some answers and information
to these topics. I really need help. And any
information would be accepted. Please help me
in the following:
1. Anne leaves town A traveling by bike to town B

[snip]
Quote:  2. Show that there is no perfect square whose digits
sum of to 2006. (7 points)
3. Two natural numbers, x and y, are taken such that
their sum is less than 100.

[snip]
Quote:  Pam: I cannot determine the sum of the numbers.
Sam: I know.
Pam: Now, I know their sum.
Sam: Now, I know their product.
Determine x and y.
PLEASE help me with whatever you can! Thank you!

You forgot to tell us how many points #1, #3, and the
last problem are worth.
Dave L. Renfro 

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Bob111 science forum Guru Wannabe
Joined: 13 Jan 2006
Posts: 115

Posted: Thu Jul 13, 2006 2:45 am Post subject:
Re: Word Problems



On Wed, 12 Jul 2006 17:05:38 EDT, Alex <ATerezi@yahoo.com> wrote:
Quote:  Hello! I would just like some answers and information to these topics. I really need help. And any information would be accepted. Please help me in the following:
1. Anne leaves town A traveling by bike to town B along a certain path at sunrise. Bart leaves town B travelling by bike to town A along the same path as Anne. They travel at a constant speed, and do not stop biking towards their final destinations. The cross each other's paths at noon. Anne gets to town B at 5:00pm and Bart gets to town A at 11:15pm. At what time was sunrise?

You'll get the best help when you show what you have done so far, so
we can focus on where you are stuck.
In this case, start with drawing a picture.
There is one central relationship: distance = rate * time. Think about
what you know.
bob 

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jasen science forum beginner
Joined: 28 Jun 2006
Posts: 16

Posted: Thu Jul 13, 2006 9:35 am Post subject:
Re: Word Problems



On 20060712, Alex <ATerezi@yahoo.com> wrote:
Quote:  Hello! I would just like some answers and information to these topics. I really need help. And any information would be accepted. Please help me in the following:
1. Anne leaves town A traveling by bike to town B along a certain path at sunrise. Bart leaves town B travelling by bike to town A along the same path as Anne. They travel at a constant speed, and do not stop biking towards their final destinations. The cross each other's paths at noon. Anne gets to town B at 5:00pm and Bart gets to town A at 11:15pm. At what time was sunrise?

write a system of simultaneous equations and solve them.
Quote:  2. Show that there is no perfect square whose digits sum of to 2006. (7 points)

It may be easier to show that there is no perfect square expressible
as 3n+2 (with n integer), and then to show that all (positive) numbers whose digits sum
to 3n+2 are expressible as 3n+2 (with different integer n),
Quote:  3. Two natural numbers, x and y, are taken such that their sum is
less than 100. (x + y < 100) Both x and y are greater than 1.
Sam is told the sum of the numbers (x + y) and Pam is told the
product of the numbers (xy). Neither of them knows the original
two numbers, x and y. They have the following conversation:
Pam: I cannot determine the sum of the numbers.
Sam: I know.

sam _knows_ from the sum that atleast one of the numbers must be
composite. (that is, not a prime number)
This means that his number is not expressible as the sum of two primes.
Quote:  Pam: Now, I know their sum.

this information tells pam howto factor the product uniquely.
(there are likely only a few ways to factor her number)
Quote:  Sam: Now, I know their product.

this information tells sam how to split his sum.
Quote:  Determine x and y.

you're looking for pam's number a number that cannot be expressed as a
product of two factors with a sum less than 100 that matches the sum of any
two primes.
Quote:  PLEASE help me with whatever you can! Thank you!

If I gave you the answers that wouldn't help.
Bye.
Jasen 

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Alex111 science forum beginner
Joined: 08 Feb 2006
Posts: 17

Posted: Thu Jul 13, 2006 8:51 pm Post subject:
Re: Word Problems



Whoops! Sorry, but #1 and #3 are also 7 Points, if that help anything... 

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Alex111 science forum beginner
Joined: 08 Feb 2006
Posts: 17

Posted: Thu Jul 13, 2006 8:53 pm Post subject:
Re: Word Problems



Wow! I am amazed! First of all, nothing there even tried to help me because I didn't understand it. Second, helping me is the best way, I don't know why you guys don't even do that... 

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Dave L. Renfro science forum Guru
Joined: 29 Apr 2005
Posts: 570

Posted: Thu Jul 13, 2006 10:00 pm Post subject:
Re: Word Problems



Alex wrote (in part):
Quote:  First of all, nothing there even tried to help me
because I didn't understand it.

?? "nothing there even tried to help me"
nothing > no one ??
there > xxxx ??
Attempt at translation: "no one even tried to help me"
?? "because I didn't understand it"
You're saying that *because* you didn't understand it,
then no one tried to help you. This doesn't make sense.
Maybe you meant the converse: If no one tried to help
you, then you didn't understand it. This makes a little
more sense, but not much.
Dave L. Renfro 

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Bob111 science forum Guru Wannabe
Joined: 13 Jan 2006
Posts: 115

Posted: Fri Jul 14, 2006 2:27 am Post subject:
Re: Word Problems



On Thu, 13 Jul 2006 16:53:53 EDT, Alex <ATerezi@yahoo.com> wrote:
Quote:  Wow! I am amazed! First of all, nothing there even tried to help me because I didn't understand it. Second, helping me is the best way, I don't know why you guys don't even do that...

Huh? At least two people gave you info to get you started. (myself and
Jason). You made no reply to either. Did you get them??
The real problem is that you didn’t give us much to work with  just
typed out a bunch of questions. Nothing is gained by us doing them.
The point is for you to learn how. If you want a dialog on how to do
them, you need to be an active participant.
bob 

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Alex111 science forum beginner
Joined: 08 Feb 2006
Posts: 17

Posted: Sat Jul 15, 2006 8:41 am Post subject:
Re: Word Problems



A dialog? Right... 

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