SOLUTION: the sum of each pair of positive integers X,Y that satisfy 3X + 4Y = 50 is computed. What is the largest such sum?

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Question 1054816: the sum of each pair of positive integers X,Y that satisfy 3X + 4Y = 50 is computed. What is the largest such sum?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
4Y=50-3X
The right hand side must be even to be divisible by 2 so X must be even.
Then only every other one is divisible by 4.
So then starting at X=2, you get 4Y=50-6=44,Y=11
So then X=6,
X=10
X=14 are also values that satisfy.
When X%3E16 they are no longer a pair of positive integers.
So then,
(2,11) :2%2B11=13
(6,8):6%2B8=14
(10,5):10%2B5=15
(14,2):14%2B2=16