On a certain test, the student gets 3 points for each correct answer and loses 2 points for each incorrect answer. The test has 37 questions total. (no question can be lfet blank.) If x is the number of answers a students gets correct, write and express fro the students total score on the test.
3x - 2(37-x)
To calculate the student's total score on the test, we need to use the given information that each correct answer earns them 3 points and each incorrect answer deducts 2 points.
Let's first define the variables:
x = number of correct answers
t = total score on the test
Now, we can express the student's total score using the given conditions:
t = 3x - 2(37 - x)
Here's how we derive this expression:
- The student's total score is the sum of the points earned for correct answers minus the points deducted for incorrect answers.
- The number of correct answers is represented by x.
- The number of incorrect answers is the difference between the total number of questions (37) and the number of correct answers (37 - x).
- Each correct answer earns 3 points, so multiplying the number of correct answers by 3 gives us the points earned for correct answers: 3x.
- Each incorrect answer deducts 2 points, so multiplying the number of incorrect answers by -2 gives us the points deducted for incorrect answers: -2(37 - x).
Simplifying the expression:
t = 3x - 2(37 - x)
t = 3x - 74 + 2x
t = 5x - 74
Now, we have the expression "t = 5x - 74" which represents the student's total score on the test in terms of the number of correct answers, x.