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A teacher gave a test, and most of his students did poorly. The teacher decided to let the students correct the questions they got wrong for 70% credit. One student corrected 80% and received a final score of 85%. What was this students initial score before corrections?

Kris
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    What are your thoughts? Simply pasting an assignment is no proper way to ask a question here. – MvG Mar 14 '13 at 21:14

1 Answers1

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Let $c$=the correct answers originally.

Let $w$=the wrong answers originally.

Let $s$=the original score.

I will express percentages as decimals.

$s=\frac c {c+w}$ (Because $c+w$ is the total number of answers.)

The student corrected $.8w$ answers. He got back $.7 \times (.8w)$ points. He still had his $c$ points. This means that $$ \frac {.7 \times (.8w)+c} {c+w} = .85$$ I quick plug into wolfram alpha gets us $\frac {29} {44}=65.\overline{90}\% \approx $66%

That student was a failure.

Christopher King
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