Hi

divide 224 into two parts

Let x and (224-x) represent the smaller and larger part respectively

Question states***

  

Solving for x

    2(224-x) = 4x + x^2   |Multiplying thru by 2x

    x^2 +6x -448 = 0 







  x = 18.3776    | Tossing out negative solution

  CHECKING our Answer***

   205.6224/18.3776 = 11.1888 = 2 + (1/2)18.3776 = 2 + 9.1888

    

Answer by htmentor(1343)   (Show Source): You can put this solution on YOUR website!
 Let the two numbers be x and y

Then we have  (1)

This step is a little tricky.  We are told the quotient is 2 and the remainder is half the denominator (the smaller number).  The expression can be written 

 (2).  

This might be hard to follow, so let's use an example:  Separating the terms, we have .  

This says that the quotient is 2 with a remainder of 3, which is half the denominator (the smaller part).

Solving for x in (2) gives  or .

Substituting into (1) gives  or  -> .

Therefore .

So the smaller part is 64 and the larger part is 160.

Check: 160/64 = 2, with a remainder of 160-2*64 = 160-128=32, which is half of 64. 

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