a test 50 problems on it. for every correct answer, 2 points are given. for each incorrect answer, 1 point is subtracted. sue scored 85 points. how many problems did she miss?
assuming she answered all the questions, and got x wrong, then there were (50-x) correct.
2(50-x) - x = 85
Now just find x.
Let's assume that Sue answered X number of questions correctly.
For each correct answer, 2 points are given. Therefore, the number of points Sue earned from the correct answers is 2X.
For each incorrect answer, 1 point is subtracted. So, the number of points Sue lost from the incorrect answers is X.
We know that Sue scored 85 points. Therefore, the equation can be written as:
2X - X = 85
Simplifying the equation:
X = 85
Therefore, Sue answered 85 questions correctly.
Since there were 50 problems in total, the number of problems she missed can be calculated as:
Number of problems missed = Total number of problems - Number of problems answered correctly
= 50 - 85
= -35
It is not possible to have a negative number of problems missed. Therefore, Sue did not miss any problems.
So, Sue answered all 50 problems.
To find out how many problems Sue missed, we need to determine her total number of correct answers. Let's assume that Sue missed 'x' problems.
Given that she scored a total of 85 points, we can set up the equation:
2 * (number of correct answers) - 1 * (number of incorrect answers) = 85
Since each question accounts for either a correct or incorrect answer, we can conclude:
(number of correct answers) + (number of incorrect answers) = total number of problems
Now, let's rewrite the equation using these terms:
2 * (number of correct answers) - 1 * (number of problems - number of correct answers) = 85
Simplifying the equation:
2 * (number of correct answers) - (number of problems - number of correct answers) = 85
Expanding the equation:
2 * (number of correct answers) - number of problems + number of correct answers = 85
Combining like terms:
3 * (number of correct answers) - number of problems = 85
Rearranging the equation to isolate the number of problems:
3 * (number of correct answers) = number of problems + 85
(number of correct answers) = (number of problems + 85) / 3
Now, let's substitute 'x' for the number of problems Sue missed:
(number of correct answers) = (x + 85) / 3
Since each correct answer earns 2 points, the total number of correct answers multiplied by 2 should be equal to Sue's score:
2 * (number of correct answers) = 85
Substituting the expression for the number of correct answers:
2 * ((x + 85) / 3) = 85
Simplifying the equation further:
(x + 85) / 3 = 85 / 2
Cross-multiplying:
2 * (x + 85) = 3 * 85
2x + 170 = 255
Subtracting 170 from both sides:
2x = 85
Dividing by 2:
x = 85 / 2
x = 42.5
Since the number of problems cannot be fractional, we conclude that Sue missed 42 problems.