Question

To win a trivia game, Nathan must score at least 75 points. Each correct answer is worth 2 1/2 points , and each incorrect answer is worth - 1/4 point. If he gets 35 questions correct and 32 questions incorrect, how many points does he have?

Answer 1

Answer:

He scored $79\frac{1}{2}$ points.

Step-by-step explanation:

Given:

Number of points for a correct answer = $2\frac{1}{2}$

Number of points scored for an incorrect answer = $-\frac{1}{4}$

Therefore, for 35 correct answers, points scored = $35\times 2\frac{1}{2}=35\times \frac{5}{2}=\frac{175}{2}$

Now, for 32 incorrect answers, points scored = $32\times -\frac{1}{4}=-\frac{32}{4}=-8$

Therefore, net number of points scored by Nathan is:

$\frac{175}{2}-8=\frac{175}{2}-\frac{16}{2}=\frac{175-16}{2}=\frac{159}{2}=79\frac{1}{2}$

Therefore, Nathan scored $79\frac{1}{2}$ points.