Question

On a television game show, contestants earn 5 points for each correct answer, but lose 2 points for each wrong answer. On last week's show, the winning contestant earned 80 points and answered 30 questions. Given that x represents the number of questions answered correctly, and y represents the number of questions answered incorrectly, determine which system of equations correctly represents this situation.

Answer 1

5x-2y =80

x+y=30

Explanation:

This situation can be represented by a system of two linear equations, with one equation representing the number of points earned and one equation representing the number of questions answered.

First, determine the equation representing the number of points earned.

Since contestants earn 5 points for every correct answer and x is the number of questions answered correctly, 5x represents the amount of points earned from correct responses. Since contestants lose 2 points for every incorrect answer and y is the number of questions answered incorrectly, 2y represents the amount of points lost from incorrect responses.

The amount of points earned minus the amount of points lost yields the total number of points at the end of the game, 80.

Next, determine the equation representing the number of questions answered.

Since x represents the number of questions answered correctly and y represents the number of questions answered incorrectly, the sum of these values equals the total number of questions, 30.

Together, these two equations create the system that can be used to determine the number of questions answered correctly and the number of questions answered incorrectly by the contestant in this situation.

Answer 2

5x-2y =80

x+y=30

Explanation:

Basically, 5x is the points earned by correct questions (5 points per right answer) and -2x is the points lost by wrong answers (2 points taken away for every wrong answer). The total points the contestant earned is 80, which is why we set this equation equal to 80. Hence, 5x-2y=80.

They also tell us that the contestant answered a total of 30 questions, so x and y combined would be the total number of questions. Hence, x+y=30.