+0  
 
0
89
1
avatar

I pick two whole numbers x and y between 1 and 10 inclusive (not necessarily distinct). My friend picks two numbers x -4 and 3y-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?

 Jun 4, 2022
 #1
avatar+2448 
0

We have the following equation: \(xy + 1 = (x-4)(3y-1)\)

 

SImplifying the right hand side and isolating the constant gives us: \(-3 = 2xy - x - 12y\)

 

From here, we can factor out \(2y\) from the right-hand side of the equation. This gives us: \(-3 = 2y(x-6) - x\).

 

Now, notice how if we add 6 to both sides of the equation, we can factor in terms of \((x - 6)\)\(3 = (2y - 1)(x-6)\)

 

Now, we need 1 term to equal 3, and the other to equal 1. There are 2 ways to do this, but only 1 will satisfy the question. 

 

Can you take it from here?

 Jun 4, 2022

24 Online Users

avatar
avatar
avatar