SOLUTION: A student takes a test where 3 points are given for every correct answer and 2 points are deducted for every wrong answer. If the students scores 55 points on a 40 question test, h
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Question 648173: A student takes a test where 3 points are given for every correct answer and 2 points are deducted for every wrong answer. If the students scores 55 points on a 40 question test, how many questions did she answer correctly? Answer by DrBeeee(684) (Show Source):
You can put this solution on YOUR website! Let r = number of problems answered correctly
Let w = number of problems answered incorrectly
From the problem statements we have
(1) r + w = 40, that is there were 40 total problem.
(2) 3*r - 2*w = 55, the grade is +3 for each correct answer and -2 for each incorrect answer. Make sense?
Solve (1) and (2) simultaneously.
Let's substitute r from (1) in (2);
(3) r = 40 - w
Then (2) becomes
(4) 3*(40-w) - 2*w = 55 or
(5) 120 -3*w - 2*w = 55 or
(6) 5*w = 65 or
(7) w = 13
Then from (3)
(8) r = 27
Is this correct? Let's see. Use (2),
Is (3*27 - 2*13 = 55)?
Is (81 - 26 = 55)?
Is (55 = 55)? Yes
Answer: The student missed 13 questions, but answered 27 correctly!
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