Challenge Schools A and B are competing in an academic contest. Correct answers earn 8 points. Incorrect answers lose 2 points. In the final round, School A gives the same number of correct and incorrect answers. School B gives no incorrect answers and the same number of correct answers as School A. School A started the final round with 58 points. School B started with 36 . The game ends with the two schools tied. Let x represent the number of correct answers given by School A in the final round. Write an equation that models the outcome of the contest. Then find the number of answers that each school got correct in the final round.

To model the outcome of the contest, we first establish the points for each school based on their correct and incorrect answers. For School A, they give x correct answers and x incorrect answers. The points for School A can be calculated as follows: Starting points + (points for correct answers) - (points lost for incorrect answers) = 58 + (8x) - (2x) = 58 + 6x. For School B, since they give the same number of correct answers (x) and no incorrect answers, their points can be calculated as: Starting points + (points for correct answers) = 36 + (8x). Since the game ends with the two schools tied, we set their points equal to each other: 58 + 6x = 36 + 8x. Now we can solve for x: 58 - 36 = 8x - 6x 22 = 2x x = 11. Thus, each school got 11 correct answers in the final round. School A had 11 correct and 11 incorrect answers, while School B had 11 correct answers with no incorrect ones. In summary: - School A's final points: 58 + (6*11) = 58 + 66 = 124 points. - School B's final points: 36 + (8*11) = 36 + 88 = 124 points. Both schools ended with 124 points, confirming they are tied!