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 1055297: 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!
So then re-writing,
y=%2850-3x%29%2F4
y=25%2F2-%283%2F4%29x
So then substituting,
x%2By=x%2B%2825%2F2-%283%2F4%29x%29
x%2By=25%2F2%2Bx%2F4
This function has a maximum value with the largest value of x that is still a positive integer.
x=14 and y=2 are the largest positive data pair and lead to the maximum sum.
S%5Bmax%5D=14%2B2=16
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