SOLUTION: in a survey 144 people, 83 people said they liked eggs, 65 people said they liked toast, 30 said they liked neither. how many people like both? a 34 b 71 c 18 d 114

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Question 1102594: in a survey 144 people, 83 people said they liked eggs, 65 people said they liked toast, 30 said they liked neither. how many people like both?
a 34
b 71
c 18
d 114
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

144 people total
30 said they don't like eggs and don't like toast
144 - 30 = 114 people like one item or the other (or both)

Let x = amount of people who like both
83 like eggs
65 like toast
x like both
83+65-x = 114
148-x = 114
148-x-148 = 114-148
-x = -34
x = 34

Answer: Choice A) 34 people like both eggs and toast

Side Note: I'm using the idea
n(A or B) = n(A) + n(B) - n(A and B)
where
n(A or B) = number of people who like A or B
n(A and B) = number of people who like A and B
n(A) = number of people who like A
n(B) = number of people who like B