#### Answer

$b=\frac{453}{8}$

#### Work Step by Step

We start with the given equation: $\frac{b}{3}+\frac{1}{8}=\frac{19}{1}$
We multiply by the least common denominator, 24: $24(\frac{b}{3}+\frac{1}{8}=\frac{19}{1})$
We apply the distributive property: $8b+3=456$
We subtract $3$ on each side of the equation: $8b+3-3=456-3$
We combine like terms: $8b=453$
Finally, we divide by $8$ on each side of the equation: $b=\frac{453}{8}$