This seems easy but I don't get it

if x and y are positive integers such that 5x + 3y = 100,

what is the greatest possible value of xy?

The greatest possible product would be if x and y are the same value so let's try that.

If x = y then 5x + 3y = 8x = 100 which ends up making x =12.5 which is not an integer.

Let's move away 1 unit and try x = 11

That would give us 5x = 55 and therefore 3y = 45 ...... that'll work

So, if I'm right       x = 11

                            y = 15

       therefore     xy = 165

.

Thanks!