Suppose you get question X right the first time and question 27-X right the second time.

6X-(20-X)× 1 =(27-X)× 10-[ 12-(27-X)]×2+22

6X-20+X=270- 10X+30-2X+22

7X-20=322- 12X

19X=342

X=342÷ 19

X= 18

The first score:18× 6-(20-18 )×1=106 (score).

Second score: (27-18) ×10-[12-(27-18) ]× 2 = 84 (points).