Question

A 24 question mathematics exam is worth 100 points. There are fill-in-the-blank questions worth 2 points each, multiple choice questions worth 6 points each, and long answer questions worth 5 points each. The number of fill-in-the-blank questions plus the number of multiple choice questions is equal to the number of long answer questions. How many of each question is on the exam?

Answer 1

If there are

x fill-in
y multiple-choice
z long-answer

they have given us the following facts:

x+y+z = 24
2x+6y+5z = 100
x+y = z

Now you can solve for x,y,z