Who Gets a Free Book and Calendar at the Book Sale?

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Homework Help Overview

The problem involves determining which individuals among the first 50 attendees at a book sale receive both a free calendar and a free book, based on the conditions that every 6th person receives a calendar and every 8th person receives a book.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the counting of individuals who receive calendars and books, with some suggesting that every 14th person receives both, while others question this reasoning. There are attempts to identify specific numbers that meet both conditions.

Discussion Status

Participants are actively engaging in counting and verifying which numbers correspond to those who receive both items. There is a mix of contributions, with some participants providing examples and others questioning the logic behind the calculations. The discussion appears to be productive, with various interpretations being explored.

Contextual Notes

There is mention of extending the problem to the first 1000 customers, indicating a potential for further exploration of the patterns involved.

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Homework Statement


Every 6th person who arrives at a book sale receives a free calendar and every 8th person receives a free book. Which of the first 50 people receive a book and a calendar?

Homework Equations


Kindly check and the solution please. Can't really figure it out.

The Attempt at a Solution


Every 14th person a free calendar and book.
 
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How did you come to this number 14 ?
 
It is my son who came up with 14. I'm not good at math unfortunately.
 
Then we do the counting: numbers 6, 12, 18 etc get a calendar.
Numbers 8, 16, etc get a book.

Continue the series and find the folks that get both !
See if there is a way to do it when they ask for the first 1000 customers ...
 
t3rom said:
It is my son who came up with 14. I'm not good at math unfortunately.

I can imagine a good, old argument in the bookstore: "my son was the 14th person in the store, so he wants his fee calendar and his free book".
 
I came up with 24 and 48. Is this correct? Thanks for helping!
 
That's the idea. Numbers like 24 and 48 can be divided by 8 and by 6.
 
t3rom said:
I came up with 24 and 48. Is this correct? Thanks for helping!

Hopefully the bookstore owner would agree with that and there would be no argument!
 

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