Overlapping Sets Problem - Word Translations book

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Pg. 127 - chapter 7 Word Translations Guide

There are 26 students who have read a total of 56 books among them. The only books they have read, though, are Aye, Bee, Cod, and Dee. If 10 students have only read Aye, and 8 students have read only Cod and Dee, what is the smallest number of books any of the remaining students could have read?

In this problem, I was having difficulty in determining the relationship between the students and books read. I understand that because the question is asking for the remaining students, the last digit in the students column should be 1. However, I would just like clarification as to why the numbers which were selected for the students and books read were chosen.

Any help on this problem would be greatly appreciated!

[jnelson0612]

Pg. 127 - chapter 7 Word Translations Guide

There are 26 students who have read a total of 56 books among them. The only books they have read, though, are Aye, Bee, Cod, and Dee. If 10 students have only read Aye, and 8 students have read only Cod and Dee, what is the smallest number of books any of the remaining students could have read?

In this problem, I was having difficulty in determining the relationship between the students and books read. I understand that because the question is asking for the remaining students, the last digit in the students column should be 1. However, I would just like clarification as to why the numbers which were selected for the students and books read were chosen.

Any help on this problem would be greatly appreciated!

Hi there,
Not totally sure that I'm understanding your question, so let me walk you through the answer and then please ask for more clarification if needed.

Okay, let's review:
4 possible books to read: A, B, C, D
26 students have read a total of 56 books

10 students have each read ONLY book A. Let's subtract 10 from both students and from books. I now have 16 students left who have read a total of 46 books.

8 students have each read ONLY C and D. Okay, so each of these 8 kids have read 2 books, or 16 books total read among the group of 8. Let's subtract 8 from students and 16 from books. That leaves us with 8 remaining students to read 30 books.

I want to know the *smallest* number of books any student could have read. I have 8 kids who HAVE to read 30 books. I want to let one lazy student read as little as possible. Can I have that lazy student read 1 book? That would mean that the other 7 would have to read 29 books. But they can't, because each student can only read four books: A,B,C,D. 7 students each reading 4 books is only 28 books. Darn. I need 29 books read. I will have to assign that extra book to the lazy student, who is already reading one book. So of the eight remaining students, the smallest possible number of books read is two.