If x and y are positive integers such that 5x+3y=100, what is the greatest possible value of xy?
We have 5x+3y=100, 6x-x+3y=100, 6x+3y=100+x, 3(2x+y)=100+x, 165?
The greatest possible value of xy will occur when x is most nearly equal to y
We have that
x y xy
17 5 85
14 10 140
11 15 165
8 20 160
So.....xy is largest when x = 11 and y = 15
