CEMC Banner

Problem of the Week
Problem B
Fun and Games

Mariana’s trivia team is playing a game against other teams. The game includes \(10\) questions, and each team is given \(5\) points to start. Teams then earn \(4\) points for each correct answer, and lose \(3\) points for each incorrect answer.

  1. The table shows the score card for Mariana’s team.

    (The trivia questions were tough!)

    In the right column, fill in their running score, which is their current score after each question.

    Question Result Running Score
    \(-\) \(-\) \(5\)
    \(1\) X
    \(2\) X
    \(3\) X
    \(4\) ✓
    \(5\) X
    \(6\) ✓
    \(7\) X
    \(8\) ✓
    \(9\) X
    \(10\) ✓

    Note that their running score may be positive or negative, like a temperature reading. You may find the following number line helpful.

    A number line with negative 5, 0, and 5 marked. There are tick marks at each integer value between negative 5 and 5.

  2. The winning team had a score of \(10\). How many questions did they get correct?

Extension: What is the maximum possible score? What is the minimum possible score? Are all the integers in between these values possible scores? Explain.

Theme: Number Sense