find the greatest possible pair of integers that one integer is twice the other and their sum is less than 30.

Less then thirty or 30 exactly?
Start with numbers that can be halved that eliminates most. Then start adding them up and try to get 30 or below thirty.
like 2 and 4 then 2+4=6 that makes it but its not the greatest it can be.
try higher numbers like 20 and 10 20+10 makes exactly thirty but its not right because it has to be less then thirty.
So since 19 won't work try 18 and its half 9. 18+9=27
wallla an answer.
I'm sure there's an easier way to do it, but I always like to think it out logically because I can't stand math.

a +b <30.
b=2a.
a +2a <30.
3a <30.
a <10.
what is the biggest integer less than ten?
nine.
a=9.
b = 2a = 2(9) =18.
b =18.
9 +18 <30.
27 <30.
true.