SOLUTION: Could you please make a system for this word problem. On a college entrance exam, each correct answer adds one point to your raw score, each unanswered question adds nothing and ea

Question 56207: Could you please make a system for this word problem. On a college entrance exam, each correct answer adds one point to your raw score, each unanswered question adds nothing and each incorrect answer subtracts 1/4 point. You answer 82 out of 85 questions for a raw score of 67. How many questions did you answer correctly? Thank you.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Could you please make a system for this word problem. On a college entrance exam, each correct answer adds one point to your raw score, each unanswered question adds nothing and each incorrect answer subtracts 1/4 point. You answer 82 out of 85 questions for a raw score of 67. How many questions did you answer correctly? Thank you.
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You didn't answer 3 questions which adds nothing to your score.
Let number of correct answers of the 82 be "x"
Number of points for those correct answers is x points.
---------------
Number of incorrect answers of the 82 is "82-x"
Number of points for those incorrect answers is (-1/4)(82-x)=(-41/2)+(1/4)x
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EQUATION:
points gained + points lost = 67
x -41/2 + (1/4)x= 67
(5/4)x = 87.5
x=70 (number of correct answers)
Cheers,
Stan H.
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