SOLUTION: in a recent survey of 400 students in a school, 100 were listed as smokers and 150 as gum chewers. 75 were listed as smokers and gum chewers. find how many students are neither smo

Question 1001702: in a recent survey of 400 students in a school, 100 were listed as smokers and 150 as gum chewers. 75 were listed as smokers and gum chewers. find how many students are neither smokers nor gum chewers.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
100 smokers
150 gum chewers
75 smokers and gum chewers.
total is 400.

formula says A or B = A + B - A and B.

A is the smokers
B is the gum chewers
A and B is the ones who do both.
A or B is the ones who do one or the other or both.

A = 100
B = 150
A and B = 75

by the formula, you get:

A or B = 100 + 150 - 75 = 250 - 75 = 175.

since there are 400 total, the ones who do neither are 400 - 175 = 225.

another way of looking at it is:

100 smokers, 75 of which chew gum as well.
break that up into:
25 smokers only.
75 smokers who chew gum also.

150 gum chewers, 75 of which smoke as well.
break that up into9:
75 who chew gum only.
75 who chew gum and smoke also.

you now have 3 categories.
25 smoke only.
75 chew gum only.
75 chew gum and smoke.

those categories are now clean, i.e. they do not include anybody who is also in another category.

add them up and you get 175.

400 - 175 = 225 which are the ones who do neither.

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