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?
2026-04-15 06:16:07.1776233767
Story Problem: Algebra
71 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
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.