jmc

First, we write out the problem in equation form:

$$\begin{array}{rl}a+2b& =15,\\ a+5b& =3.\end{array}$$

Subtracting the first equation from the second, we have $3b=-12⟹b=-4$. Then, substituting $b=-4$ into the first equation: $$\begin{array}{rl}a+2(-4)& =15,\\ a& =23.\end{array}$$ so $a+b=23-4=\boxed{19}$.