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?
If Nancy did all 10 problems and scored 18 points, how many correct answers did she have?
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problem-solving
word-problem
4 Answers
2
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 $10-3=7$.
1
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.
1
Correct answers$=x$ ,Incorrect answers$=10-x$
$3.x -1.(10-x)=18$
$4x=28$
$x=7$
0
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.