2B. In a quiz, the contestant answers 24 questions. If the contestant answers a question correctly, they earn 4 points, and if they answer incorrectly, they lose 1.4 points. How many questions did the contestant not know the answer to if they ended up with 69 points at the end of the quiz?
Solution. Let $x$ be the number of correctly answered questions, and $y$ the number of incorrectly answered questions. Clearly $x+y=24$, or $y=24-x$. On the other hand, the total number of points earned is $4x-1.4y=69$. If we substitute $y=24-x$ we have $4x-1.4(24-x)=69$ from which we find $x=19$.

Thus, the number of incorrectly answered questions is $y=24-x=24-19=5$.