Answer: From the conditions given, the total number of the problems should be 29. This means that the sum of x and y should be 29. With this and the point-system, the best system of equation that is useful for this problem is,
x + y = 29
5x + 2y = 100
Your first answer choice is the correct answer.
Fact: I suggest looking up the question before asking it because sometimes others have asked the questions and it will be answered. Just letting you know to help you save points.