# Question

A librarian bought \$2122.40 worth of books. The ratio of the number of English books she bought to the number of Chinese books was 5 : 2 . The total cost of the English books was \$1125.60 more than the total cost of the Chinese books. Each English book cost \$2.70 more than each Chinese book. How many books did the librarian buy?

Total                  Diff                      Chinese                            English

Value     \$2122.40       \$1125.60     \$996.80/2=\$498.40   \$498.40+1125.60=\$1624

Total books                                         2 units of  C-books         5 units of E-books

1 unit of C-books=\$249.20  1 unit of E-books=\$324.80

Diff=\$75.60 for each unit

Big diff/small diff = 75.60/2.70=28 (so each unit consists of 28 books)

Total no. of books = 2 units + 5 units  = 7 units  = 196 books#

Check: 249.20/28 = \$8.90 per C-book, \$11.60 per E-book

28 x 2 x 8.90 + 28 x 5 x 11.60 = \$2122.40

196 x 8.90 + 28 x 5 x 2.70 = \$2122.40

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An alternative for reference ….. but longer method.

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