There are 45 questions in an exam.for every correct answer 5 points and every wrong 3 points is deducted.if she got 185 point.how many correct answers did she get...
c = correct answes
w = wrong answe
She must answer 45 questions so the sum of right and wrong answers is 45.
c + w = 45
For every correct answer 5 marks is awarded and for every wrong answer 3 marks is deducted.
This means:
She got
c ∙ 5 - w ∙ 3 = 185 points.
Now you must solve system:
c + w = 45
5 c - 3 w = 185
____________
The solutions are:
c = 40
w = 5
40 correct answes
5 wrong answes
Checking the results.
c + w = 40 + 5 = 45
c ∙ 5 - w ∙ 3 = 40 ∙ 5 - 5 ∙ 3 = 200 - 15 = 185
Let's assume the number of correct answers as "x". Since there are 45 questions on the exam, the number of incorrect answers would be 45 - x.
For every correct answer, 5 points are awarded, so the total points earned from correct answers would be 5x.
For every incorrect answer, 3 points are deducted, so the total points deducted from incorrect answers would be 3(45 - x) or 135 - 3x.
Given that the total points earned is 185, we can set up the equation:
5x - (135 - 3x) = 185
Simplifying the equation, we get:
5x - 135 + 3x = 185
Combining like terms, we have:
8x - 135 = 185
Adding 135 to both sides of the equation:
8x = 320
Dividing both sides by 8:
x = 40
Therefore, she answered 40 questions correctly.
To find the number of correct answers, we need to solve the given problem using algebra.
Let's assume the number of correct answers as 'x'.
Since each correct answer gives 5 points, the total points earned from correct answers would be 5x.
Considering that 3 points are deducted for each incorrect answer, the total points deducted would be 3(45 - x).
The total points earned is given as 185. So, we can set up the equation as follows:
5x - 3(45 - x) = 185
Simplifying the equation gives:
5x - 3 * 45 + 3x = 185
5x - 135 + 3x = 185
8x - 135 = 185
8x = 185 + 135
8x = 320
x = 320 / 8
x = 40
Therefore, she got 40 correct answers.