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

He scored
`79(1)/(2)` points.

Explanation:

Given:

Number of points for a correct answer =
`2(1)/(2)`

Number of points scored for an incorrect answer =
`-(1)/(4)`

Therefore, for 35 correct answers, points scored =
`35* 2(1)/(2)=35* (5)/(2)=(175)/(2)`

Now, for 32 incorrect answers, points scored =
`32* -(1)/(4)=-(32)/(4)=-8`

Therefore, net number of points scored by Nathan is:

`(175)/(2)-8=(175)/(2)-(16)/(2)=(175-16)/(2)=(159)/(2)=79(1)/(2)`

Therefore, Nathan scored
`79(1)/(2)` points.