97) if the average of 3a and 4b is less than 50 and a is twice b, what
is the largest integer value of a?
a) 8
b) 9
c)10
d)11

The average of and satisfies

Then

, so if must be an integer, then the largest integer value it can take on is 19 if can be a rational number (in which case ) or 18 if must also be an integer.

Given that none of the provided answer choices lists 18 or 19, I'd bet there's a typo and you're supposed to find the maximum integer value of , in which case the answer would be B as the largest integer value would be 9.

goog may have it for you