The average of [tex]3a[/tex] and [tex]2b[/tex] satisfies
[tex]\dfrac{3a+4b}2<50[/tex]
Then
[tex]a=2b\implies\dfrac{3(2b)+4b}2=5b<50\implies b<10[/tex]
[tex]a=2b[/tex], so if [tex]a[/tex] must be an integer, then the largest integer value it can take on is 19 if [tex]b[/tex] can be a rational number (in which case [tex]b=9.5[/tex]) or 18 if [tex]b[/tex] 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 [tex]b[/tex], in which case the answer would be B as the largest integer value would be 9.
