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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?

 Mar 26, 2020

Best Answer 

 #2
avatar+21017 
+1

The product of your two numbers, x and y, must be one more than the product of your friend's numbers, (x - 4) and (2y - 1).

Putting this into an equation:  xy  =  (x - 4)(2y - 1) + 1

Multiplying out:                        xy  =  2xy - x - 8y + 4 + 1

Simplifying:                              xy  =  2xy - x - 8y + 5

Subtracting xy:                          0  =  xy - x - 8y + 5

Adding x:                                   x  =  xy - 8y + 5

Subtracting 5:                      x - 5  =  xy - 8y

Factoring:                            x - 5  =  y(x - 8)

Dividing by x - 8:    (x - 5) / (x - 8)  =  y

 

Using the formula:  y  =  (x - 5) / (x - 8).

 

Replace x with the possibilities:  1, 2, 3, ..., 10

You will find that 9 will be a possiblity for x; this will give you the value for y.

 Mar 26, 2020
 #1
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0

THX SO MUCH GENO3141!!!!!!!!!!!!! YOU ARE THE ONLY PERSON (unless cphill) THAT HELPED ME THE MOST!!!!! I APRECIATE IT!

 Mar 26, 2020
 #2
avatar+21017 
+1
Best Answer

The product of your two numbers, x and y, must be one more than the product of your friend's numbers, (x - 4) and (2y - 1).

Putting this into an equation:  xy  =  (x - 4)(2y - 1) + 1

Multiplying out:                        xy  =  2xy - x - 8y + 4 + 1

Simplifying:                              xy  =  2xy - x - 8y + 5

Subtracting xy:                          0  =  xy - x - 8y + 5

Adding x:                                   x  =  xy - 8y + 5

Subtracting 5:                      x - 5  =  xy - 8y

Factoring:                            x - 5  =  y(x - 8)

Dividing by x - 8:    (x - 5) / (x - 8)  =  y

 

Using the formula:  y  =  (x - 5) / (x - 8).

 

Replace x with the possibilities:  1, 2, 3, ..., 10

You will find that 9 will be a possiblity for x; this will give you the value for y.

geno3141 Mar 26, 2020
 #3
avatar+111330 
0

Very nice, Geno....I liked  the way you solved this one    !!!!!!

 

 

cool cool cool

CPhill  Mar 27, 2020

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