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If x and y are positive integers for which 3x + 2y + xy = 117, then what is x + y?

 Jul 12, 2022
 #1
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3x + xy + 2y = 117

x(3+y) + 2y = 117

x(3+y) + 2y + 6 = 123

x(3+y) + 2(y+3) = 123

(x+2)(y+3) = 123

 

123 = 41 x 3

x + 2 = 3 

y + 3 = 41

 

x = 1, y = 38

 

x + y = 39. 

 Jul 12, 2022

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