Method 1: Had she answered all 30 correctly, she would have scored 30(13) = 390. The effect of replacing a correct answer by an incorrect answer is a loss of 13 + 5 = 18 points. Since she actually scored 192, she answered (390-192)/18 = 11 questions incorrectly.
So Ann answered 30 - 11 = 19 questions correctly.

Method 2: Let x = number of correct answers, and y = number of incorrect answers. We have the system

1) x + y = 30
2) 13x - 5y = 192

Adding equation 2) to 5 times equation 1, we get 5x + 13x = 150 + 192.
So 18x = 342 and then x = 19.
So, again, Ann answered 19 questions correctly.

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