Question

Kering purchased (2x-1) identical pens for Ksh 180. Naraya purchased (3x+ 1) identical pencils for Ksh 200. 

1. Write an expression for the:
   • price of one pen; 
   • price of one pencil. 
2. A pen costs Ksh 4 more than a pencil. 
   Form an equation to represent the information above and hence solve for x.
3. Later the price of a pen went up by 25% while that of a pencil remained unchanged A school spent the same amount of money on the purchase of pens as that spent on pencils The total number of both pens and pencils bought was 46. Determine the number of pens bought by the school.

Answer 1

1.  
   • 1 pen =  180   
                  2x−1
   • 1 pencil =  200 
                      3x+1
2.  180    -    200     = 4
   (2x-1)     (3x+1)
   6x² − 36x − 96 = 0
   x² − 6x − 16 = 0
   (x + 2)(x − 8) = 0
   x = −2 or x = 8
3. Pen = 180    but x= 8
              2x-1
     180   = Ksh. 12
   2(8)−1
   new pen price = 1.25x12 = KSh 15
                 pencil = Ksh 8
   Let no. of pens be m and pencils be n
   m + n = 46
   15n − 8m = 0