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A trivia contest asks both multiple choice and free response questions. Contestants receive 3 points for each correct multiple choice question and 5 points for each correct free response question, and they must score more than 60 points to advance to the next round. If Eva advanced to the next round of the contest, which of the following inequalities describes 
x, the number of multiple choice questions, and 
y, the number of free response questions, that she answered correctly?
Choose 1 answer:
(A) 
3x+5y > 60
(B) 
3x+5y >= 60
(C) 
3x+5y < 60
(D) 
3x+5y <= 60

A trivia contest asks both multiple choice and free response questions. Contestants receive 33 points for each correct multiple choice question and 55 points for each correct free response question, and they must score more than 6060 points to advance to the next round. If Eva advanced to the next round of the contest, which of the following inequalities describes x x , the number of multiple choice questions, and y y , the number of free response questions, that she answered correctly?\newlineChoose 11 answer:\newline(A) 3 x+5 y>60 \newline(B) 3x+5y60 3 x+5 y \geq 60 \newline(C) 3 x+5 y<60 \newline(D) 3x+5y60 3 x+5 y \leq 60

Full solution

Q. A trivia contest asks both multiple choice and free response questions. Contestants receive 33 points for each correct multiple choice question and 55 points for each correct free response question, and they must score more than 6060 points to advance to the next round. If Eva advanced to the next round of the contest, which of the following inequalities describes x x , the number of multiple choice questions, and y y , the number of free response questions, that she answered correctly?\newlineChoose 11 answer:\newline(A) 3x+5y>60 3 x+5 y>60 \newline(B) 3x+5y60 3 x+5 y \geq 60 \newline(C) 3x+5y<60 3 x+5 y<60 \newline(D) 3x+5y60 3 x+5 y \leq 60
  1. Determine Points Earned: Determine the points earned per question type. Eva earns 33 points for each correct multiple choice question and 55 points for each correct free response question. This means that if xx is the number of multiple choice questions she gets right, she earns 3x3x points from them. Similarly, if yy is the number of free response questions she gets right, she earns 5y5y points from them.
  2. Combine Points for Total Score: Combine the points from both types of questions to find the total score. The total score Eva earns from both types of questions is the sum of the points from multiple choice questions and free response questions, which is 3x+5y3x + 5y.
  3. Condition for Advancing: Determine the condition for advancing to the next round. The problem states that contestants must score more than 6060 points to advance. This means that Eva's total score must be greater than 6060.
  4. Formulate Inequality: Formulate the inequality based on the condition for advancing. Since Eva's total score from both types of questions must be more than 6060, the inequality that represents this condition is 3x + 5y > 60.

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