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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?

 Nov 26, 2020
 #1
avatar+419 
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We have: (x-4)(2y+1)-1 = xy

 

So xy + x - 8y - 5 = 0

 

The numbers are 2 and 7 so 14.

 Nov 26, 2020
 #2
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See the detailed answer here:  https://web2.0calc.com/questions/i-pick-two-whole-numbers

 Nov 27, 2020
 #3
avatar+116126 
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xy  + 1  =  (x - 4) ( 2y + 1)

 

xy + 1 = 2xy + x - 8y - 4

 

xy + x - 8y -5  =  0

 

x ( y + 1)  =  8y + 5

 

x  =   8y + 5

       ______        x = 7   when y  = 2        

          y + 1

 

The product =  14

 

 

cool cool cool

 Nov 27, 2020

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