Jacob is playing a game where he earns 3 points for a correct answer and loses 2 points for an incorrect answer. He currently has –6 points. What situation would end with him breaking even?

Question

answering one question correctly and the last question incorrectly
answering one question incorrectly and the last question correctly
answering the last two questions correctly
answering the last two questions incorrectly

Answer 1

To determine how Jacob can break even from his current score of -6 points, we can analyze the options based on the point system: +3 points for a correct answer and -2 points for an incorrect answer.

Current situation: Jacob has -6 points.

Breaking even goal: Reach 0 points.

Analyzing the Options:

1. Answering one question correctly and the last question incorrectly:

   • Correct answer: -6 + 3 = -3 points
   • Incorrect answer: -3 - 2 = -5 points
   • Final score: -5 (not breaking even).

2. Answering one question incorrectly and the last question correctly:

   • Incorrect answer: -6 - 2 = -8 points
   • Correct answer: -8 + 3 = -5 points
   • Final score: -5 (not breaking even).

3. Answering the last two questions correctly:

   • First correct answer: -6 + 3 = -3 points
   • Second correct answer: -3 + 3 = 0 points
   • Final score: 0 (breaking even).

4. Answering the last two questions incorrectly:

   • First incorrect answer: -6 - 2 = -8 points
   • Second incorrect answer: -8 - 2 = -10 points
   • Final score: -10 (not breaking even).

Conclusion:

The only situation that results in Jacob breaking even is: Answering the last two questions correctly.