Question 1152383
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Let x be the value under the question (the original number of glasses).


Then the price for each glass when buying is  {{{300/x}}} rupees.


She made R100 profit selling, so she sold for R300 + R100 = R400.


The number of glasses sold is (x-10), according to the condition.


For each of (x-10) glasses sold, she get R4 more than paid per glass buying.


It means that


    {{{400/(x-10)}}} - {{{300/x}}} = 4.    (1)


It is your basic equation.


To solve it, multiply both sides by x*(x-10).  You will get


    400x - 300*(x-10) = 4x*(x-10).


Simplify step by step and solve


    400x - 300x + 3000 = 4x^2 - 40x

    4x^2 -40x - 100x - 3000 = 0

    4x^2 - 140x - 3000 = 0

     x^2 - 35x - 750 = 0

    (x-50)*(x+15) = 0  


Of the two roots, 50 and -15, only positive value x= 50 is the solution.


<U>ANSWER</U>.  50 glasses were bought at the price of  {{{300/50}}} = R6.


<U>CHECK</U>.  I will check that the equation (1) is valid.


        {{{400/(50-10)}}} - {{{300/50}}} = {{{400/40}}} - {{{300/50}}} = 10 - 6 = 4.    ! Precisely correct !
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Solved.


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