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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

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