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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?
 Jun 27, 2020
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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.

 Jun 27, 2020

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