SOLUTION: A school planned to buy x Calculators for a total coast of Ksh 16200 . The supplier agreed to give a discount of Ksh 60 per calculator . The school was then able to get three ext

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Question 1151690: A school planned to buy x Calculators for a total coast of Ksh 16200 . The supplier agreed to give a discount of Ksh 60 per calculator . The school was then able to get three extra calculators for the same amount of money .
(a) Write an expression in terms of x , for the:
(1)Original price of each calculator;
(2)Price of each calculator after the discount.
(b)Form an equation in x and hence determine the number of calculators the school bought.
(c) Calculate the discount offered to the school as a percentage.
Answer by ikleyn(52782) About Me  (Show Source):
You can put this solution on YOUR website!
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(a)  

    (1)   16200%2Fx.

    (2)   16200%2F%28x%2B3%29


(b)       16200%2Fx - 16200%2F%28x%2B3%29 = 60.


          To solve it, first cancel the factor 60 in both side


              270%2Fx - 270%2F%28x%2B3%29 = 1


          Multiply both sides by x*(x+3)


               270*(x+3) - 270x = x*(x+3)

               x^2 + 3x - 810 = 0

               (x+30)*(x-27) = 0.


         Of the two roots  x= -30  and  x= 27, only positive x= 27 is the solution.



(c)      Thus the number of calculators before discount was 27, 

             and the price for each single calculator was  16200%2F27 = 600.


         After discount, the number of calculators  was  27+3 = 30, 

             and the price for each single calculator was 16200%2F30 = 540.


         The discount from the price for each single calculator is  %28600-540%29%2F600 = 60%2F600 = 0.1 = 10%.

Solved.

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