# Out of 200 grade 12 students, 108 are taking Natural Math and 115 are taking Managesial Math. If 54 are taking neither, how many are taking both? How many are taking either but not both?

2
by yana3

2016-05-30T18:18:36+08:00
Given: total number of students = 200 total number of students taking Natural math = 108 total number of students taking Managesial math = 115 total number of students taking neither = 54 Required: number of students taking both math subjects number of students taking either but not both Solution: let x be the number of students taking both let y be the number of students taking nat. math let z be the number of students taking man. math y = (total n of students - n of students taking nat. math) - n of students taking neithe y = (200 - 108) - 54 y = 31 z = (total n of students - n of students taking man. math) - n of students taking neither z = (200 - 115) - 54 z = 38 x = (108 - y) or x = (115 - z) x = 77
• Brainly User
2016-06-03T10:45:02+08:00
Step 1: Taking either and both
200 - 54 = 146 students

Step 2:  Taking both
(108 + 115) - 146 = 77 students

Step 3:  Taking either but not both
A.  Taking Natural Math subject only
108 - 77 = 31 students

B.  Taking Managerial Math subject only
115 - 77 = 38  students

C.  Total number of students taking either but not both
31 + 38 = 69 students

ANSWER:  77 students are taking both subjects, while 69 students are taking neither but not both.

Check:
(Taking neither subject) + (Taking both subjects) + (Taking either but not both subjects) = 200

54 + 77 + 69 = 200

200 = 200 (True)