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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 22, 2020
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(x - 4) * (2y + 1)  = x * y + 1, solve for x, y

 

x = (8 y + 5)/(y + 1), substituting 1 for y does not give an integer.

But subbing 2 for y, we get:

x =(8*2 + 5) / (2 + 1) =21 / 3 =7

 

So, your numbers are: x = 7  and y = 2. And x * y =7 * 2 = 14

Your friend's numbers =(7 - 4) =3   and   (2*2 + 1) =5, And: 3 * 5 = 15

 Nov 22, 2020

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