[cpk]

You don't have enough information. You also need...

f: Average first-ball score. This is so you can calculate the value of spares and doubles.
o: Average open-frame score. This is so you can calculate the value of strikes followed by open frames.

Let's say p = 1 - x - s to make the representation easier

The math is now easy:

9[(10 + (10+f(1-x)+10x)x + 10s + op)x + <font color="red">strikes</font>
(10 + 10x + f(1-x))s + <font color="red">spares</font>
+ op] <font color="red">open</font>
+
(10 + (10+f(1-x)+10x)x + 10s + op)x + <font color="red">X in frame 10</font>
(10 + 10x + f(1-x))s + <font color="red">/ in frame 10</font>
op <font color="red">open</font>