Q: How many questions were answered correctly by a student who received 38 marks on an entrance exam where 3 marks were awarded for each correct answer and 1 mark was deducted for each wrong answer, given that the total number of questions was 70?  

 To solve this problem, we can use the fact that the total number of 
marks a student receives is equal to the number of correct answers multiplied by 3, minus the
 number of wrong answers. We can represent this relationship with the equation:

3x - y = 38

Where x is the number of correct answers and y is the number of wrong answers.

We are also given that the total number of questions is 70, so we can set up
 a second equation to represent this relationship:

x + y = 70

We can solve this system of equations by first solving for y in the first equation:

y = 3x - 38

Substituting this expression for y into the second equation gives:

x + (3x - 38) = 70

This simplifies to:

4x - 38 = 70

Adding 38 to both sides gives:

4x = 108

Dividing both sides by 4 gives:

x = 27

Therefore, the student answered 27 questions correctly.