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Miko has a vast collection of her collection. (5)/(7) of the remaining books are Chinese books and the rest are German books. How many books are there in her book collection if there are 75 Chinese books? books

Miko has a vast collection of her collection. (5)/(7)(5)/(7) of the remaining books are Chinese books and the rest are German books. How many books are there in her book collection if there are 7575 Chinese books?

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Q. Miko has a vast collection of her collection. (5)/(7)(5)/(7) of the remaining books are Chinese books and the rest are German books. How many books are there in her book collection if there are 7575 Chinese books?
  1. Calculate Fraction of Chinese Books: Let's find out what fraction of Miko's collection is Chinese books.\newlineWe know that 57\frac{5}{7} of the remaining books are Chinese, and there are 7575 Chinese books.\newlineSo, we can write the equation (57)×(remaining books)=75\left(\frac{5}{7}\right) \times (\text{remaining books}) = 75.
  2. Solve for Remaining Books: Solve for the remaining books.\newline(remaining books)=75(5/7)(\text{remaining books}) = \frac{75}{(5/7)}\newline(remaining books)=75×(75)(\text{remaining books}) = 75 \times (\frac{7}{5})\newline(remaining books)=15×7(\text{remaining books}) = 15 \times 7\newline(remaining books)=105(\text{remaining books}) = 105
  3. Find Total Number of Books: Now, we need to find out the total number of books in Miko's collection.\newlineSince 57\frac{5}{7} are Chinese, 27\frac{2}{7} must be German books.\newlineSo, the total books are the sum of Chinese and German books.\newlineBut we made a mistake here; we don't need to calculate the German books separately. We already have the total remaining books, which includes both Chinese and German books.

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