We are told that two schools take part in an academic contest. School A starts with 165 points and gives the same number of correct and incorrect answers. School B starts with 65 points and gives the same number of correct answers as School A. We want to determine which equations describes the scoring in the final round. Let's start with defining x.
x - &the number of correct answers
&made by School A
Let's now express both schools' scores in terms of x. School A already has 165 points. Each correct answer gives them 12 points and each incorrect answer loses them 5 points. Therefore, their score will be the number of correct answers x multiplied by 12 minus the number of incorrect answers, also x, multiplied by 5 plus 165.
School A's score: 12x- 5x+ 165
School B already has 65 points. Each correct answer also gives them 12 points and each incorrect answer loses them 5 points. Their score will be the number of correct answers, x, multiplied by 12 plus 65. Since School B gives only correct answers they do not have any points subtracted. Note that the number of correct answers is x, because the schools gave the same number of correct answers.
School B's score: 12x+ 65
We now that the games end with two scores tied, so they need to be equal. Therefore, we need to make an equation that will have School A's score on the left-hand side and School B's score on the right-hand side.
12x- 5x+ 165 = 12x+ 65
The obtained equation corresponds to option B.
Now we want to find the number of answers each school got correct. Note that both schools got the same number of correct answers, which we marked as x. To find this number we need to solve the equation found in the previous part of the exercise. To do so, we will use the inverse operations to combine like terms on both sides of the equals sign and solve for x.
