Question

Alexandra scored 40 on an exam, receiving 3 points for each right answer and losing 1 point for each wrong answer. Had 4 points been given for each right answer and 2 points deducted for each wrong answer, Alexandra would have scored 50. How many questions were on the exam

Answer 1

Answer: there were 20 questions in the exam.

Step-by-step explanation:

Let x represent the number of right answers.

Let y represent the number of wrong answers.

Alexandra scored 40 on an exam, receiving 3 points for each right answer and losing 1 point for each wrong answer. It means that

3x - y = 40- - - - - - - - - - 1

Had 4 points been given for each right answer and 2 points deducted for each wrong answer, Alexandra would have scored 50. It means that

4x - 2y = 50- - - - - - - - - - -2

Multiplying equation 1 by 2 and equation 2 by 1, it becomes

6x - 2y = 80

4x - 2y = 50

Subtracting both equations, it becomes

2x = 30

x = 30/2

x = 15

Substituting x = 15 into equation 1, it becomes

3 × 15 - y = 40

45 - y = 40

y = 45 - 40

y = 5

The number of questions in the exam is

x + y = 15 + 5 = 20