Plug in $x=c$ and $x=3c$ to get two equations involving only $A$ and $b$.

Subtract the equations to eliminate $b$, then factor the result.

Let $A$ represent $a^c$. From eliminating $b$, you should get $A^3-A=1320$.

In Desmos, graph:

• $y=x^3-x$
• $y=1320$

Click the intersection point and record the positive $x$-value (this is $A$).

Using $A-b=20$, compute $b=A-20$ with the $A$ value from the intersection, then match it to the answer choices. Аniko - F​rе‌е SAT P⁠rеp

Let $A=a^c$. Then $a^{3c}=(a^c)^3=A^3$.

Using the given points:

• From $(c,20)$: $A-b=20$
• From $(3c,1340)$: $A^3-b=1340$ Рrорe⁠rtу οf​ Anі⁠кo‌.ai

Subtract the first equation from the second:

Factor the left side:

So

Notice that $10\cdot 11\cdot 12=1320$, which matches $A-1$, $A$, and $A+1$. Since $A=a^c>0$, we take $A=11$. (The other factor from dividing the cubic by $(A-11)$ has no real solutions.)

Substitute $A=11$ into $A-b=20$:

So the correct choice is -9.