
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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June 3rd, 2019, 04:19 PM  #1 
Senior Member Joined: Jan 2012 Posts: 745 Thanks: 7  How many correct answers did she get?
In a mathematics quiz, each correct answer gets 2 marks and a wrong answer attracts 1. Kevwe got a total of 19 in a quiz with 20 questions. How many correct answers did she get? I don’t seem to understand the problem. If she has 19marks and 2 marks is for each correct answer, I will say that she got 9 questions correct which fetched her (9 x 2) marks = 18 marks. I don’t know how the other 1 mark came about that made it 19 marks. By asking how many correct answers she got, I understand it to mean how many questions she answered correctly that gave 19 marks total. Is my understanding correct? if not I need better understanding to this problem. 
June 3rd, 2019, 04:28 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,549 Thanks: 1399 
basically we're talking about two equations There are 20 total questions, Kevwe gets every question either right or wrong. $r+w=20$ Right answers are +2 points, wrong answers are 1 points. Kevwe scored 19. $2rw=19$ It's easy enough to solve this, add the two equations. $3r = 39$ $r=13$ $w=20r = 7$ Kevwe got 13 questions correct, and 7 incorrect. 
June 4th, 2019, 01:48 AM  #3 
Senior Member Joined: Jan 2012 Posts: 745 Thanks: 7 
Thanks for the explanation and equation so far. I just want to ask some few questions: Does this mean that for every question she answers wrongly, 1 mark will be subtracted from the scores she already have? Apart from using equation, are there other ways this can be solved? 
June 4th, 2019, 02:41 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,966 Thanks: 2216 
Had all 20 questions been answered wrongly, the total marks would have been 20. For each question answered correctly, 2 marks are awarded and one negative mark isn't awarded, making a total improvement of 3 marks. As she got a total of 19 marks, and 19  (20) = 39, she got 39/3 = 13 questions correct.

June 4th, 2019, 05:49 AM  #5  
Senior Member Joined: Jan 2012 Posts: 745 Thanks: 7  Quote:
Quote:
Last edited by skipjack; June 4th, 2019 at 01:15 PM.  
June 4th, 2019, 09:26 AM  #6  
Senior Member Joined: Sep 2015 From: USA Posts: 2,549 Thanks: 1399  Quote:
13×2  7 = 26  7 = 19 2 × 13 = 26, not 36 Last edited by skipjack; June 4th, 2019 at 01:16 PM.  
June 4th, 2019, 10:21 AM  #7 
Senior Member Joined: Jan 2012 Posts: 745 Thanks: 7 
Suppose she had all the 20 questions correct what would be her score?

June 4th, 2019, 11:47 AM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  
June 4th, 2019, 01:22 PM  #9  
Global Moderator Joined: Dec 2006 Posts: 20,966 Thanks: 2216  Quote:
so the number of wrong answers was (40  19)/3 = 7, which means the number of correct answers was 20  7 = 13.  

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