Ann, a very competitive person, decides to give herself 2 points for every crossword puzzle in her daily newspaper that she completes correctly and takes away 3 points for every crossword in the paper that she completes incorrectly or cannot complete. after 30 days of working the puzzles, ann has a score of zero. how many puzzles has she solved correctly?

You can set two equations with two unknown variables.

Call x the number of crossword puzzles completed correctly.

Call y the number of crosswor puzzles completed incorrectly or not completed.

After 30 days of working:

(1) x + y = 30    < number of crossword

(2) 2x - 3y = 0   < points

From (1) x = 30 - y

replace  x in (2) => 2(30 - y)  - 3y = 0

solve:

60 - 2y - 3y = 0

60 - 5y = 0

5y = 60

y = 60/5

y = 12  < not completed or incorrectly completed

x = 30 - 12 = 18 < correctly completed

Then, the answer is that she has solved 18 puzzles correctly

Wait hold on lemme think