If 164 of the 400 eighth-graders take none of these courses, then 400-164=236 students take some courses.
Let x students take all three courses, then:
1. 70-x take only both algebra and advanced computer,
2. 34-x take only both algebra and industrial technology,
3. 29-x take only both advanced computer and industrial technology.
Now let's count how many student take only one course:
1. 117-(x+34-x+70-x)=13+x take algebra,
2. 109-(x+29-x+70-x)=10+x take advanced computer,
3. 114-(x+29-x+34-x)=51+x take industrial technology.
Now count all students that take some courses:
51+x+10+x+13+x+29-x+34-x+70-x+x=236,
x=236-51-10-13-29-34-70,
x=29.
Answer: all three courses take 29 students.
