In a math contest of 10 problems, 3 points are given for each correct answer and 1 point is deducted for each incorrect answer. If Nancy did all 10 problems and scored 18 points, how many correct answers did she have?
closed as off-topic by Namaste, Shailesh, TheGeekGreek, TravisJ, JonMark Perry Feb 9 '17 at 7:41
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She answered $10$ questions, so she was expecting $30$ points. Instead, she got only $18$ points. That means that she lost a total of $12$ points. If you take into consideration that an incorrect answer takes $4$ points from your expected total ($3$ for annulment, $1$ for penalty), the amount of incorrect answers is $12/4=3$. That means that the number of correct answers is $10-3=7$.
Correct answers$=x$ ,Incorrect answers$=10-x$
Let $x$ be correct answers then $10-x$ are incorrect answers.
Then marks for correct answers = $3 × x = 3x$
And marks deducted for incorrect answers = $1 × (10-x) = 10 - x$
Now after deducting negative marks she got 18 marks.
$3x - (10-x) = 18$
$3x - 10 + x = 18$
$4x = 28$
$x = 7$
So correct answers 7 and incorrect answers 3.
Suppose she had 6 correct answers. That's $6 \times 3 - 4 = 18-4 = 14$. Nope too low!
What about 7? $7 \times 3 - 3 = 21-3 = 18$. Oh, we got it.