# A bookseller bought a certain number of books for 337.50 and sold some of them at the cost price 213.75. Find the least number of books left with him.

hustoncmk | Certified Educator

The first step in this problem is determining the cost per book. To do this you must find the greatest common factor of each of the two numbers given.

The factors of 337.50 = 5 x 5 x .05 x 9 x 30

The factors of 213.75 = 5 x 5 x .05 x 9 x 19

When you multiply the common factors you get  11.25 which equals the cost of the book. At this cost the bookseller bought 30 books and sold 19, leaving a balance of 111 books.

I hope that this helps you understand the problem more clearly.

neela | Student

The cost price of the certain number of books = 337.50

cost of some books the buyer sold  = 213.75.

The cost of the remaing number of books = 337.5-213.75 = 123.75.

To determine  the least number of books left with him.

Let us now assume x is the price of the book. The number of books now remmaing could a miminimum iff x is the highest possible price, Or

x  is the greatest common factor of (123.75 , 213.75 and 337.5).

We shall find the GCF between 123.75 and 213.75.

123.75(213.75(1

123.75

--------------------

90 ) 123.75 (1

90.00

------------------

33.75)90.00(2

67.50

-----------------------------

22.50) 33.75(1

22.50

-------------------------------------

11. 25)22.5(2

22.50

............................................................

0

Therefore the GCF (213.75 , 33.50) is 11.25 which is the greatest possible price and the least possible he purchase is 337.5/11.25 = 30 books. And the number of books he sold for cost price is 213.75/11.25 = 19 books.

So the remaing books = 30-19  = 11books.

So the greatest possible price is t