Books

[som]

I have a math task and I really understand nothing :!:- I am also unsure if I am here in the right thread.

I hope someone can help!!! And may explain a little bit....

"In his bookcase, John has a collection of fve books from the same publishing house. Each book was published and purchased two years after the previous one. When John tries to determine how long he has had them, he realizes that the sum of the number of years he has owned each book is 100. How many years ago was the last book in John's collection published?"

 

[som]

Word Problem - and it's clear to me as mud... PLS help !

[h=2]Have a math task/question and it's as clear as mud to me ... PLS help ![/h]

I have a math task and I really understand nothing :!:- I am also unsure if I am here in the right thread.

I hope someone can help!!! And may explain a little bit....

"In his bookcase, John has a collection of fve books from the same publishing house. Each book was published and purchased two years after the previous one. When John tries to determine how long he has had them, he realizes that the sum of the number of years he has owned each book is 100. How many years ago was the last book in John's collection published?"​

 

[Deleted member 4993]

I have a math task and I really understand nothing :!:- I am also unsure if I am here in the right thread.

I hope someone can help!!! And may explain a little bit....

"In his bookcase, John has a collection of fve books from the same publishing house. Each book was published and purchased two years after the previous one. When John tries to determine how long he has had them, he realizes that the sum of the number of years he has owned each book is 100. How many years ago was the last book in John's collection published?"

If you understand nothing - why are you taking this class?

You do under stand that this question:

Is dealing with a series (arithmetic progression), and,

there are 5 terms in the series, and,

the common difference of the series is 2 and

the sum of the series is 100.

Assume that

the last book (the 5 th book) was published and purchased L years ago.

the fourth book was published and purchased (L+2) years ago

the third book was published and purchased (???) years ago
.....
the first book was published and purchased (???) years ago

continue...

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[mmm4444bot]

Well, it's your thread, heh, heh. I think you meant 'board'. S'okay -- we can move a thread to another board later if needed.

One start is to be certain that you understand the given scenario and what form the answer should take. That makes sense, yes? You need to know what the question is asking for.

After that, you may begin eliminating information that's superfluous (i.e., not relevant) and focus on what's relevant.

For example, we don't really need to care about things like where the books were published or whether they are part of a collection or where John stores them in his house, and it's clear that the publishing dates and purchase dates are the same, so we may simply think in terms of purchases. We have a sense that we need to add up some numbers; that's what the question is asking for: a total.

EG:

John bought five books. He purchased them two years apart. John realizes that the sum of the number of years he has owned each book is 100. How many years ago did he buy the most recent book?

Do you have any experience with algebra or math terminology? For example, is it clear to you that the word 'sum' indicates that you need to add the year counts for a grand total?

You could make a chart, and play with numbers. Make a guess, like maybe John has owned the most recently-purchased book for 22 years. Then the book purchased before that has been his for 24 years, and the one before that for 26 years, and so on. Add 'em up; see how close to 100 you get. Adjust your guess, and try again.

Algebra is a system of language notation and rules for expressing mathematical relationships as equations using symbol to represent unknown stuff that we'd like to find and for solving such equations.

So, you could also pick a symbol, like R, to represent exactly what the question is asking for: the number of years since the most recent book was published (which we know is the same as the purchase year).

Let R = number of years since the most-recent purchase

Then R + 2 is the number of years since the purchase immediately before, just like 22 + 2 is 24 years in the guess above. Two years before that? R + 4.

Adding the five expressions that represent the year counts and setting it equal to 100 gives an equation to solve for R.

Does this help you? I don't yet know the context of your task. Cheers :cool:

EDIT: OIC, we're not on the Odds & Ends Board anymore, Dorothy! We were merged into a duplicate universe, as I typed.

 

[som]

Haha

Haha - Sure I understand a little bit but the point that he has the books already 100 years is really confusing me. Of course I understand that the books are all published 2 years after the previous one - I am not completely stupid but I anyway don't get the point with the 100 years !???

And I don't take a class it's in a book to prepare for tests (work!)....

I don't know how he can own the books 100 years ?? Is he so old ??

Sorry, you can think about me whatever you want (stupid, helpless, blind... whatever the choice is yours) but I don't get it (and anyway ENGLISH is NOT my NATIVE language that makes everything much more complicated!!).
However - I would say 10 years ago... But it's wrong I know, but everything else I cannot explain (there are 5 choices - I forgot )

- 16 years
- 14 years
- 10 years
- 8 years
- 4 years

... so 10... Am I right? -No, probably not, that would be too easy I guess.

I just think very, very simple and go two years back but HOW the .... the 100 is related to that all?!? I don'T get it ^^

 

[mmm4444bot]

Haha

I am not completely stupid

I am sorry that you read our posts that way. Gosh. I cannot read minds. I do not know anything about you. I did not think that you are stupid; I thought that you were having fun with brain-teasers.

And I don't take a class it's in a book to prepare for tests (work!)

What job makes you take this test?

If there is a language barrier also, then this bulletin board may not be the best place for you. Math discussion requires clear communication. I'm not sure how to explain the 100 years again. It is a total. 100 years is what you get when you add up all the years John has owned five books.

Cheers :cool:

 

[mmm4444bot]

I would say 10 years ago... But it's wrong I know

... so 10... Am I right? -No, probably not, that would be too easy I guess.

Let's see what happens with 10 years, as a guess.

5th book: 10 years
4th book: 12 years
3rd book: 14 years
2nd book: 16 years
1st book: 18 years

10 + 12 + 14 + 16 + 18 = 70

You are correct; 10 years is not the correct answer. The year counts need to add up to 100. :cool:

 

[som]

no - actually not you, your pre-writer made me feel a little bit like a dumb "Why are you taking this class?!". Yeah, even if I would take a class, that would be great and nothing to criticize....

Dunno why my post sounds so negative, wasn't meant like that.

It's in English because I would like to get an internship (in the US) - and may you can agree that my English is not that bad. At least I hope so. Okay. And the book (self printed) is provided by the company. So ... I have to find the solution and better yet understand it :/

So, I am sorry - let's start new, please.

.... Why 100? Sum up what??? I mean, the books are published with an interval of 2 years. That makes sense so far. That means that the 5 books have been published in (total) 10 years. That I all get - But why 100?! Sum up what? Why he owns the books 100 years?! .... Huh ?


Thanks

 

[Deleted member 4993]

no - actually not you, your pre-writer made me feel a little bit like a dumb "Why are you taking this class?!". Yeah, even if I would take a class, that would be great and nothing to criticize....

Dunno why my post sounds so negative, wasn't meant like that.

It's in English because I would like to get an internship (in the US) - and may you can agree that my English is not that bad. At least I hope so. Okay. And the book (self printed) is provided by the company. So ... I have to find the solution and better yet understand it :/

So, I am sorry - let's start new, please.

.... Why 100? Sum up what??? I mean, the books are published with an interval of 2 years. That makes sense so far. That means that the 5 books have been published in (total) 10 years. That I all get - But why 100?! Sum up what? Why he owns the books 100 years?! .... Huh ?


Thanks

Sum up what ? - MMM has explained that by giving you an example in the previous post.

Why 100? - That is given to you - it is a data point - there is no "why" to it. It is like asking why a given club has 42 members.

Let us start with the hint I gave you before (and you did not work with it)

Let

the last (5th) book be published "L" year before (This is what we need to "find")

Then the 4 th book was published "L+2" year before

the 3 rd book was published "L+4" year before

the 2 nd book was published "L+6" year before

the 1 st book was published "L+8" year before

Then, we are given:

L + (L+2) + (L+4) + (L+6) + (L+8) = 100

Now solve for "L"

 

[mmm4444bot]

the books are published with an interval of 2 years

↑ Change "the books" to "adjacent books"


That means that the 5 books have been published in (total) 10 years ← Yes, but they have not been published for 10 years. That's the distinction.

Maybe the authors of this exercise are intentionally trying to trick you by talking about publications and purchases at the same time. That is why I suggested that you strip away all of the extra junk in the given "wordy problem".

This scenario of book publishing and purchasing could have started when John was 5 years old, or 25 years old, or 85 years old. How old is John, today? We don't know any of this, but we do know that all of the years that John owned those books add up to 100 years.

You must realize that many of these years are being counted more than once, when we add the years that each book has been owned.



I wish you good fortune! Cheers :cool: