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I pick two whole numbers $x$ and $y$ between $1$ and $10$ inclusive (not necessarily distinct). My friend picks two numbers $x -4$ and $2y-1$. If the product of my friend's numbers is one greater than the product of my numbers, then what is the product of my numbers?

 Apr 16, 2021
 #6
avatar+118666 
+1

(x - 4)  ( 2y - 1)  =  xy  + 1       simplify

 

2xy  - x - 8y  +  4  =  xy + 1

 

xy  - x - 8y  +  3   =  0

 

xy - x  =   8y  - 3

 

x ( y - 1)  =  8y - 3

 

x =    (8y - 3)  /  ( y - 1)

 

Notice  that if   y  =  6,  then  x =  9

 

The product of  your friends  numbers  =  (5)(11) = 55

 

The product of your  numbers  =  9 * 6   =   54

 

cool cool cool

 Apr 16, 2021

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