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

To solve this problem, let's first set up the equation based on the given information. If School A gets \(x\) correct answers, then it also gives \(x\) incorrect answers. For School A, the score from the final round will be calculated as follows: starting points (58) + points from correct answers (8x) - points from incorrect answers (2x). This gives us the equation for School A's final score as: \[ \text{Score of School A} = 58 + (8x - 2x) = 58 + 6x \] For School B, since they get the same number of correct answers \(x\) and no incorrect answers, their final score becomes: \[ \text{Score of School B} = 40 + 8x \] Since the two schools end up tied, we can set their scores equal to each other: \[ 58 + 6x = 40 + 8x \] Now, let’s solve for \(x\): 1. Rearranging the equation gives: \[ 58 - 40 = 8x - 6x \] 2. This simplifies to: \[ 18 = 2x \] 3. Dividing by 2, we find: \[ x = 9 \] So, both schools answered 9 questions correctly in the final round! Now, School A answered 9 correct and 9 incorrect, while School B answered 9 correct and 0 incorrect. In summary, School A has a final score of \(58 + 6(9) = 102\), and School B has a final score of \(40 + 8(9) = 102\), confirming they indeed end up tied!