Kosuke wrote a mathematics contest consistingof 25 multiple choice questions, the scoring system gave 6 points for a correct answer, 2 points for not answering, and 1 point for an incorrect answer.Kosuke got x correct and left y unanswered questions
a) write an expression for the number of questions he answered correctly
b) write an expression , in simplifed form, for Kosuke's score
What is confusing. The problem says, "Kosuke got x correct" and then asks for "an expression for the number of questions he answered correctly "
Ummm, x?
For the score, just multiply the points by each type of question:
If there were 25 questions, and he answered x and left y unanswered, then that means that the remainder 25-(x+y) were wrong:
score = 6x + 2y + (25 - (x + y))
= 6x + 2y + 25 - x - y
= 25 + 5x + y
a) The number of questions Kosuke answered correctly can be represented by the expression "x".
b) Kosuke's score can be calculated as follows:
Total score for correct answers = Number of correct answers * Points for correct answer = 6x
Total score for unanswered questions = Number of unanswered questions * Points for not answering = 2y
Total score for incorrect answers = Number of incorrect answers * Points for incorrect answer = 1(25 - x - y)
Kosuke's score = Total score for correct answers + Total score for unanswered questions + Total score for incorrect answers
= 6x + 2y + 1(25 - x - y)
Simplifying the expression:
Kosuke's score = 6x + 2y + 25 - x - y
= 5x + y + 25
a) The number of questions Kosuke answered correctly can be represented by the variable x.
b) To calculate Kosuke's score, we need to consider the points awarded for correct answers, unanswered questions, and incorrect answers.
For the correct answers, Kosuke earned 6 points for each question. Since he answered x questions correctly, the score for the correct answers is 6x.
For the unanswered questions, Kosuke earned 2 points for each question. Since he left y questions unanswered, the score for the unanswered questions is 2y.
For the incorrect answers, Kosuke earned 1 point for each question. However, we don't have information about the number of incorrect answers, so we cannot include this in the expression for his score.
Therefore, the expression for Kosuke's score, in simplified form, is 6x + 2y.
a) The number of questions Kosuke answered correctly can be represented by the variable x.
b) Kosuke's score can be calculated by multiplying the number of questions answered correctly by the point value for a correct answer, adding the product of the number of unanswered questions and the point value for not answering, and finally adding the product of the number of incorrect answers and the point value for an incorrect answer. In this case, the expression for Kosuke's score would be:
Score = (x * 6) + (y * 2) + ((25 - x - y) * 1)
Simplifying this expression further:
Score = 6x + 2y + (25 - x - y)
= 6x + 2y + 25 - x - y
= 5x + y + 25