Question 1062877: Can you help with the following problem please?
On a college entrance exam, you answered 80 of 85 questions. Each correct answer adds 1 point to your raw score, each unanswered question adds nothing, and each incorrect answer subtracts 1/4 point. Your raw score was 70. How many questions did you answer correctly?
What I did was set up a table with x being the number of correct questions with a value of 1, then a row for wrong questions giving that the variable of y, with a value of -0.25. The column of variables x + y was equal to 80, the total number of questions answered. The 85 was irrelevant since no points were added or subtracted for unanswered questions. So equation 1 is x + y = 80. The second equation I made was from the totals column which was x times 1, plus y times -0.25 equals 70, the raw score. I then solved equation 1 x+y = 80 for x. X = 80 - y. Then I used the second formula (x * 1)+ (y * (-0.25)) = 70 and tried to solve substituting the value 80-y for x from the first equation. I cannot make a go of it from here. Am I using the wrong method to set this up?
Thank you!
Found 2 solutions by jorel1380, MathTherapy:
Answer by jorel1380(3719)   (Show Source):
You can put this solution on YOUR website! Let c be your correct answers, and i be your incorrect answers. Then:
c + i=80
c-.25i=70
So:
4c-i = 280
c + i=80
Adding them, we get:
5c=360
c=72
You answered 72 questions correctly, and 8 questions incorrectly. ☺☺☺☺
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Can you help with the following problem please?
On a college entrance exam, you answered 80 of 85 questions. Each correct answer adds 1 point to your raw score, each unanswered question adds nothing, and each incorrect answer subtracts 1/4 point. Your raw score was 70. How many questions did you answer correctly?
What I did was set up a table with x being the number of correct questions with a value of 1, then a row for wrong questions giving that the variable of y, with a value of -0.25. The column of variables x + y was equal to 80, the total number of questions answered. The 85 was irrelevant since no points were added or subtracted for unanswered questions. So equation 1 is x + y = 80. The second equation I made was from the totals column which was x times 1, plus y times -0.25 equals 70, the raw score. I then solved equation 1 x+y = 80 for x. X = 80 - y. Then I used the second formula (x * 1)+ (y * (-0.25)) = 70 and tried to solve substituting the value 80-y for x from the first equation. I cannot make a go of it from here. Am I using the wrong method to set this up?
Thank you!
I prefer to use C for number of correct answers and I for number of incorrect answers.
Anyway, you got the following 2 equations:
x + y = 80______x = 80 - y ------- eq (i)
x - .25y = 70 ------ eq (ii)
You decided to use SUBSTITUTION, and your 1st equation: x = 80 - y is set up as the value for x to substitute.
Therefore, you would substitute this in eq (ii) to get: 80 - y - .25y = 70
- 1.25y = 70 - 80
- 1.25y = - 10
y, or number of INCORRECT answers =  . Now subtract 8 from 80 (questions answered) to get 72 (80 - 8) correct answers.
Since the substitution you did (for x) resulted in a value for y: the INCORRECT answers, and then you still had to calculate the CORRECT answers,
I would've opted to solve the 1st equation for y to get: y = 80 - x. This way, you would've gotten the value for x, the number of CORRECT answers, without doing another calculation.
|
|
|
