Question 221931
Since 35 students are in algebra, and 18 are in both, this means that 35-18=17 students are in algebra only. 


Also, because 52 students are in history, and 18 in both classes, there are 52-18=34 students in just history alone.


Now add up the number of students in algebra only (17), the number of students in history only (34), and the number of students in both (18) to get: 17+34+18=69


So there are 69 students in either class or both. Now subtract this figure from 100 to find the number of students who are in neither class: 100-69=31


So there are 31 students in neither class.