Suppose that $a$ and $b$ are positive real numbers, and let
\[f(x) = \begin{cases} \frac{a}{b}x & \text{ if }x\le-4, \\ abx^2 & \text{ if }x>-4. \end{cases} \]
If $f(-4)=-\frac{60}{13}$ and $f(4)=3120$, what is $a+b$?
a/b * (-4) = -60/13 divide both sides by -4
a/b = 15/13 → a = (15/13)b
ab *4 = 3120 divide both sides by 4
ab = 780
(15/13)b * b = 780
b^2 = 780*13/15
b^2 = 676 take the square root
b = 26
a = (15/13) b = (15/13) (26) = 30
a + b = 30 + 26 = 56
+230 
