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In order to win a quiz contest, Olga must score more than 400 points. She earns 12 points for each right answer, and loses 4 points for each wrong answer.
Write an inequality that represents the number of right answers 
(R) and wrong answers 
(W) Olga can give to win the contest.

In order to win a quiz contest, Olga must score more than 400400 points. She earns 1212 points for each right answer, and loses 44 points for each wrong answer.\newlineWrite an inequality that represents the number of right answers (R)(R) and wrong answers (W)(W) Olga can give to win the contest.

Full solution

Q. In order to win a quiz contest, Olga must score more than 400400 points. She earns 1212 points for each right answer, and loses 44 points for each wrong answer.\newlineWrite an inequality that represents the number of right answers (R)(R) and wrong answers (W)(W) Olga can give to win the contest.
  1. Identify Points: Identify the points Olga earns for each right answer and loses for each wrong answer.\newlineOlga earns 1212 points for each right answer and loses 44 points for each wrong answer.
  2. Set up Inequality: Set up an inequality to represent the total points Olga must score to win the contest.\newlineOlga must score more than 400400 points to win the contest.
  3. Translate to Algebraic Inequality: Translate the given information into an algebraic inequality.\newlineThe total points Olga scores is the sum of the points from right answers minus the points lost from wrong answers. This total must be greater than 400400.\newlineSo, the inequality is 12R - 4W > 400.
  4. Check Inequality: Check the inequality to ensure it represents the situation correctly.\newlineFor each right answer, Olga's score increases by 1212 points, and for each wrong answer, her score decreases by 44 points. The inequality 12R - 4W > 400 correctly represents the condition that Olga's score must be more than 400400 points to win.

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