The 2007 AMC 10 will be scored by awarding $6$ points for each correct response, $0$ points for each incorrect response, and $1.5$ points for each problem left unanswered. After looking over the $25$ problems, Sarah has decided to attempt the first $22$ and leave only the last $3$ unanswered. How many of the first $22$ problems must she solve correctly in order to score at least $100$ points?

Rayjplayz Jun 27, 2020

#1**0 **

Because she will get 1.5 points for each question left unanswered and she leaves 3 questions unanswered,

she will receive 3 x 1.5 points = 4.5 points.

To get at least 100 points, she will need 100 - 4.5 points = 95.5 points on the first 22 questions.

Since she gets 6 points for each correct answer, she will need 95.5 / 6 = 15.92 correct answers --->

she will need 16 correct answers.

16 x 6 = 96 points + 4.5 points = 100.5 points.

geno3141 Jun 27, 2020