The inequality that represents the number of right answers (r) and wrong answers (w) Olga can give to win the contest is: [tex]3r-w>100[/tex]
Explanation
Number of right answers is [tex]r[/tex] and number of wrong answers is [tex]w[/tex]
Olga earns 12 points for each right answer and loses 4 points for each wrong answer.
So, total points earned for [tex]r[/tex] right answers [tex]=12r[/tex]
and total points lost for [tex]w[/tex] wrong answers [tex]=4w[/tex]
That means, her score will be: [tex](12r-4w)[/tex] points.
In order to win the quiz contest, Olga must score more than 400 points. So, the inequality will be.......
[tex]12r-4w>400\\ \\4(3r-w)>400\\ \\ 3r-w>100[/tex]
