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.

We begin by letting x be the number of correct answers School A gives in the final round. According to the problem, School A also gives x incorrect answers. (A correct answer is worth 8 points and an incorrect answer deducts 2 points.) Step 1. Write the expression for School A’s points in the final round. • Points gained from x correct answers: 8x • Points lost from x incorrect answers: 2x • Net addition for School A: 8x – 2x = 6x Since School A started with 58 points, School A’s final score is:   58 + 6x Step 2. Write the expression for School B’s points in the final round. School B gives no incorrect answers and gives the same number (x) of correct answers. Therefore, School B earns:   8x points in the final round. If School B started with 40 points (this is the missing piece of information in the statement), School B’s final score becomes:   40 + 8x Step 3. Set up the equation for the two schools being tied. Since the game ended with the two schools tied, we have:   58 + 6x = 40 + 8x Step 4. Solve the equation. Subtract 6x from both sides:   58 = 40 + 2x Subtract 40 from both sides:   18 = 2x Divide both sides by 2:   x = 9 Thus, each school got 9 correct answers in the final round. In summary: • The equation is: 58 + 6x = 40 + 8x • Solving gives x = 9 correct answers for each school in the final round.