There are 45 questions in an exam. For every correct answer 5 marks awarded and for every wrong answer 3 marks are deducted. Melissa scored 185 marks. How many correct answers did she give?
c = correct answers
w = wrong answers
Since there are 45 questions on the exam, it means that the sum of correct and wrong answers is 45.
c + w = 45
5 marks awarded for every correct answers , 3 marks are deducted for every wrong answers answers and Melissa scored 185 marks means:
5 c - 3 w = 185
Now you must solve system:
c + w = 45
5 c - 3 w = 185
____________
Try to solve this.
The solutions are:
c = 40 , w = 5
40 correct answers and 5 wrong answers.
Check results:
40 ∙ 5 - 5 ∙ 3 = 200 - 15 = 185
Well, let's find out! We know that Melissa scored 185 marks, and for every correct answer, she gets 5 marks. So, let's start with the maximum number of correct answers Melissa could have given.
If Melissa answered all 45 questions correctly, she would get 5 marks for each question, which is a total of 225 marks. However, if we assume that Melissa gets all the questions wrong, she would lose 3 marks for each question, which is a total loss of 135 marks.
Now, we subtract the total loss from the maximum possible score: 225 - 135 = 90.
So, Melissa has 90 marks that are not accounted for. Since each correct answer gives her 5 marks, we can divide the remaining marks by 5 to find the number of correct answers: 90 / 5 = 18.
Therefore, Melissa gave 18 correct answers.
Let's assume Melissa answered 'x' questions correctly.
For every correct answer, 5 marks are awarded, so the total marks contributed by correct answers would be 5x.
There are 45 questions in total, so the remaining (45 - x) questions would be answered incorrectly.
For every wrong answer, 3 marks are deducted, so the total marks deducted for wrong answers would be 3(45 - x).
Given that Melissa scored a total of 185 marks, we can form the equation:
5x - 3(45 - x) = 185
Now let's solve for 'x'.
5x - 135 + 3x = 185
8x - 135 = 185
8x = 185 + 135
8x = 320
x = 320 / 8
x = 40
Therefore, Melissa correctly answered 40 questions.
To find out how many correct answers Melissa gave, let's assume that she gave 'x' correct answers out of the total of 45 questions.
Since for every correct answer, 5 marks are awarded, the total marks awarded for the correct answers would be 5 * x.
Since for every wrong answer, 3 marks are deducted, the total marks deducted for the wrong answers would be 3 * (45 - x). (Remember, the number of wrong answers can be calculated as the difference between the total number of questions and the number of correct answers.)
Now, let's calculate the total marks scored by Melissa:
Total Marks = Marks Awarded for Correct Answers - Marks Deducted for Wrong Answers
185 = 5x - 3(45 - x)
Let's solve this equation to find the value of x, which represents the number of correct answers.
185 = 5x - 135 + 3x
185 = 8x - 135
8x = 185 + 135
8x = 320
x = 320 / 8
x = 40
Therefore, Melissa gave 40 correct answers.