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- Thread starter ryan_kidz
- Start date
First write everything down as fractions under a common denominator.
For example, \(\displaystyle \frac{68}{884}\) is a frac for the biographies. Do the same for the atlases and the books.
Then, add up the biographies and atlases. Simplify the fraction and you will get the sum of the books that are either biographies or atlases.
For example, \(\displaystyle \frac{68}{884}\) is a frac for the biographies. Do the same for the atlases and the books.
Then, add up the biographies and atlases. Simplify the fraction and you will get the sum of the books that are either biographies or atlases.
Simple logic, books can only be i whole number quantities. You can have two or three but never 2.5 books.
25% are fiction - that means the number of books is divisible by four
1/13 are biographies - thaty means the number of books is divisible by 13
1/17 are atlases - that means the number of books is divisble by 17
Now your task is simple...find a whole number between 1000 and 2000 that is divisible by 4, 13 and 15
25% are fiction - that means the number of books is divisible by four
1/13 are biographies - thaty means the number of books is divisible by 13
1/17 are atlases - that means the number of books is divisble by 17
Now your task is simple...find a whole number between 1000 and 2000 that is divisible by 4, 13 and 15
Hello, ryan_kidz!
Then \(\displaystyle \frac{N}{4}\) are fiction, \(\displaystyle \frac{N}{13}\) are biographies, \(\displaystyle \frac{N}{17}\) are atlases.
These comprise: .\(\displaystyle \frac{N}{4}\ +\ \frac{N}{13}\ +\ \frac{N}{17} \:= \:\frac{341N}{884}\) books.
Since this number is a positive integer, \(\displaystyle N\) must be a multiple of \(\displaystyle 884.\) *
The only multiple of 884 between 1000 and 2000 is: \(\displaystyle N\ =\ 1768.\)
You can finish the problem now.
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* . since .\(\displaystyle \frac{341}{884} \:= \:\frac{11\cdot31}{4\cdot13\cdot17}\) .cannot be reduced.
Let \(\displaystyle N\) be the total number of books in the library: \(\displaystyle 1000 \leq N \leq 2000\)The library in Johson City has between 1000 and 2000 books.
Of these, 25% are fiction, 1/13 are biographies, and 1/17 are atlases.
How many books are either biographies or atlases?
Then \(\displaystyle \frac{N}{4}\) are fiction, \(\displaystyle \frac{N}{13}\) are biographies, \(\displaystyle \frac{N}{17}\) are atlases.
These comprise: .\(\displaystyle \frac{N}{4}\ +\ \frac{N}{13}\ +\ \frac{N}{17} \:= \:\frac{341N}{884}\) books.
Since this number is a positive integer, \(\displaystyle N\) must be a multiple of \(\displaystyle 884.\) *
The only multiple of 884 between 1000 and 2000 is: \(\displaystyle N\ =\ 1768.\)
You can finish the problem now.
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* . since .\(\displaystyle \frac{341}{884} \:= \:\frac{11\cdot31}{4\cdot13\cdot17}\) .cannot be reduced.