Miko has a vast collection of books in her library. English books make up 8 3 of her collection. 7 5 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

Question

Miko has a vast collection of books in her library. English books make up  8 3 ​   of her collection.  7 5 ​   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

Bytelearn · Accepted Answer

Calculate Fraction of Chinese Books: Let's find out what fraction of Miko's collection is Chinese books. We know that 5/7 of the remaining books are Chinese, and there are 75 Chinese books. So, we can write the equation (5/7) * (remaining books) = 75.Solve for Remaining Books: Solve for the remaining books. (remaining books) = 75 / (5/7) (remaining books) = 75 * (7/5) (remaining books) = 15 * 7 (remaining books) = 105Find Total Number of Books: Now, we need to find out the total number of books in Miko's collection. Since 5/7 are Chinese, 2/7 must be German books. So, the total books are the sum of Chinese and German books. But 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.

Miko has a vast collection of books in her library. English books make up $\frac{3}{8}$ of her collection. $\frac{5}{7}$ 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? $\newline$ $\square$ books

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