+0  
 
0
45
2
avatar

The sum of the product and the sum of two positive integers is 39. Find the largest possible value of the product of their sum and their product.

 Sep 10, 2022
 #1
avatar
0

nevermind. found it by factoring

 Sep 10, 2022
 #2
avatar+2444 
0

\(x + y+ xy = 39\)

\(x( 1 + y) + y = 39\)

\(x(1+y) + 1 + y = 39 + 1\)

\(x(1+y) + 1(1+y) = 40\)

\((x+1)(y+1)=40\)

 

The only pairs that work are \((0,39)\)\((1, 19)\)\((3, 9)\), and \((4, 7)\)

 

The product of sums and products are 0, 380, 324, and 308. 

 

So, the largest possible value is \(\color{brown}\boxed{380}\)

 Sep 11, 2022
edited by BuilderBoi  Sep 11, 2022

16 Online Users