Question

A bookseller bought a number of cartons of books at a cost of ksh 57600 from Kagumo bookstore. Had he bought the same books from Kerugoya bookstore, it would have cost him ksh 480 less per carton. This would have enabled him to buy 4 extra cartons of books for the same amount of money. By taking x to be the number of cartons of books he actually bought;

1. write an expression in x
   1. for the cost of each carton he bought at Kagumo bookstore
   2. for the cost of each carton had he bought from Kerugoya bookstore 
2. find the value of x 
3. The bookseller later sold all the books he had bought each carton at ksh 720 more than he had paid for it. Determine the percentage profit he made

Answer 1

1.  
   1. 57600             
          x
   2. 57600  − 480  
                 x
2. No. of cartons bought from Kerugoya bookstore = x + 4    
   (x + 4) ( 57600  − 480)  = 57600    
              (          x           )
   57600 − 480x + 230400 − 1920 = 57600  
                                      x
   55680x − 480x² + 230400 =57600x    
   −1920x −480x² +230400 =0
   x² + 4x − 480 =0                     
    x² − 20x+ 24x − 480 =0
   x( x−20) + 24(x−20) =0
   x=20
   x=−24       
   No of cartons = 20    
3. 720 × 20  × 100 =25%
     57600