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

 Apr 22, 2018
 #1
avatar+101088 
+2

10xy + 14x + 15y  = 166     simplify as 

 

5y ( 2x + 3)  =  166 - 14x

 

Since the left side is divisible by 5, then so is the right side

 

When  x  =  4

 

5y (2*4 + 3)  =  166 - 14 * 4

 

5y (11)  =  166 - 56

 

55y  = 110

 

y  =  2

 

So  x  + y  =   4 + 2  =  6

 

 

 

cool cool cool

 Apr 22, 2018
 #2
avatar+982 
+3

Never seen a problem like this before.

 

Well done!

GYanggg  Apr 22, 2018
 #3
avatar+164 
+2

THANKS CPHILL :DDDD

 Apr 22, 2018

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