SOLUTION: A student loses a mark for every wrong answer and scores 2 marks for every correct answer. If the answers all the 60 questions in an exam. and secure 39 marks, how many of them wer

Question 1113041: A student loses a mark for every wrong answer and scores 2 marks for every correct answer. If the answers all the 60 questions in an exam. and secure 39 marks, how many of them were correct
Found 3 solutions by ikleyn, stanbon, greenestamps:
Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
.
1. - Two equations setup and solution

x + y = 60 (1) 2x - y = 39 (2) ---------------------------Add eq(1) and (2) to eliminate y. You will get 3x = 60+39 = 99 ====> x = = 33. Answer. 33 correct answers. The rest 60-33 = 27 answers are incorrect. Check. 2*33 - 27 = 39. ! OK !

2 - One equation setup and solution

2x - (60-x) = 39. 3x = 39 + 60 = 99 ====> x = = 33 the same answer.

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
A student loses a mark for every wrong answer and scores 2 marks for every correct answer. If the answers all the 60 questions in an exam. and secure 39 marks, how many of them were correct.
-------------
c + w = 60 questions
2c-w = 39 marks
-----------------------
Add and solve for "c":
3c = 99
c = 33 (# of correct answers)
---
w = 60-33 = 27 (# of wrong answers)
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Cheers,
Stan H.
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Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Here is a method of solving this kind of problem without algebra, using some logical reasoning.

(1) If all 60 questions were answered correctly, the student would score 120 marks; the actual score was 39 marks, which is 81 less than 120.

(2) Each wrong answer decreases the score by 3 (you lose 2 points for not having the right answer, and another point for having the wrong answer).

(3) The number of wrong answers must then be 81/3 = 27.

(4) And then the number of right answers must be 60-27 = 33.
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