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For (x,y), positive integers, let \(10xy+14x+15y=166\) . Find \(x+y\).

mathtoo  Aug 25, 2018
 #1
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10xy  + 14x + 15y  = 166

 

Note that  ( 2x + 3) ( 5y + 7)   =

 

10xy + 15y + 14x + 21  =  166 + 21      factor the left side

 

(2x + 3) ( 5y + 7)  = 187

 

Note that  187  factors as  11 * 17

 

So....we can let  x = 4   and y  = 2   and we get

 

(2*4 + 3)  (5*2 + 7) =

  (11)     (17)  =     187

 

So

 

10 (4 * 2)  + 14(4) + 15(2)  =

80  + 56 + 30  =

80 + 86  =

166

 

 

And x + y  = 4 + 2   = 6

 

cool cool cool

CPhill  Aug 25, 2018
edited by CPhill  Aug 25, 2018

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