SOLUTION: Of the 29 vendors at a farmers' market, there are 6 that sell carrots and 13 that sell tomatoes. If 3 of the vendors sell both carrots and tomatoes, how many of them sell neither c

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Question 1121832: Of the 29 vendors at a farmers' market, there are 6 that sell carrots and 13 that sell tomatoes. If 3 of the vendors sell both carrots and tomatoes, how many of them sell neither carrots nor tomatoes?

Found 3 solutions by Boreal, MathTherapy, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
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carrots alone is 3
tomatoes alone is 10
both c and t are 3
That leaves 16 that sell neither.

Answer by MathTherapy(10552) About Me  (Show Source):
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Of the 29 vendors at a farmers' market, there are 6 that sell carrots and 13 that sell tomatoes. If 3 of the vendors sell both carrots and tomatoes, how many of them sell neither carrots nor tomatoes? 
Correct answer: 13.

Accept NO OTHER!

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
The number of vendors who sell EITHER carrots OR tomatoes is  6 + 13 - 3 = 16.



    I subtracted 3 from the sum of 6 + 13, because those who cell both carrots and tomatoes were counted twice in this sum.



Hence,  the number of vendors who sell NEITHER carrots NOR tomatoes is  29 - 16 = 13.


See the lesson
    - Counting elements in sub-sets of a given finite set
in this site.