A teacher has just completed writing the final examination for his course in mathematics. This examination has 12 questions, whose total value is to be 200 points. In how many ways can the teacher assign the 200 points if each question must count for at least 10, but not more than 25 points and the point value for each question is to be a multiple of 5?
I would like to know what is wrong in the starting point of my solution:
This is equivalent to finding the integer solutions to
5(x1 + x2 + … + x12) = 200 <=> x1 + x2 + … + x12 = 200/5 <=> x1 + x2 + … + x12 = 40
where 10/5 ≤ xi/5 < 25/5 <=> 2 ≤ xi ≤ 5
for all 1 ≤ i ≤ 12.