1. In a contest, $\mathbf{30}$ problems are given. For each correct answer, 5 points are awarded, and for each wrong answer, 3 points are deducted. How many correct answers did a student give who scored 118 points?
## Solution and Grading Criteria:

Assuming the student answered all questions correctly .......................................... $1 \mathrm{p}$

a) How many points would the assumption yield?

$30 \cdot 5=150$ points

b) What is the difference between the obtained score and the actual score?

$150-118=32$ points $1 \mathrm{p}$

c) What is the bonus points awarded for a wrong answer?

$3+5=8$ points

..............................................................................

d) How many wrong answers are there?

$32: 8=4$ wrong answers

$1 p$

e) How many correct answers are there?

$30-4=26$

...............................................................................1p

Verification: $26 \cdot 5-4 \cdot 3=130-12=118$ points

$1 \mathrm{p}$