SOLUTION: A group of 35 students performed in a school program. out of the 35,18 sang,19,danced, and 7 sang and danced Venn diagram​. thank you

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Question 1183899: A group of 35 students performed in a school program. out of the 35,18 sang,19,danced, and 7 sang and danced Venn diagram​. thank you
Found 3 solutions by Theo, greenestamps, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
you are stating that.....

there are a total of 35 students.

18 sang
19 danced
7 sand and danced.

your numbers don't add up.

first of all.

if there are 35 students total, and 18 of them sang and 19 of them danced, that gets you a total of 37 students, assuming that none of hem both sang and danced.

in order for there to be 35 students total, 2 of them must have sang and danced.

that would give you 16 who sang only and 17 who danced only and 2 who sang and danced for a total of 35 students.

if you had 18 students who sang and 19 students who danced and 7 who sang and danced, and the 7 who sang and danced were included in the number of those who sang and those who danced, then you would get:

11 sand only and 12 danced only and 7 sang and danced.

that would give you a total of 30 students.

if you had 18 students who sang and 19 students who danced and 7 who sand and danced, and the 7 who sand and danced were not included in the number of those who sang and those who danced, then you would get:

18 sand only and 19 danced only and 7 sang and danced.

that would give you a total of 44 students.

bottom line:

you have a prblem with your numbers.

it could not be 35 students.
it would only be 30 or 44.

here are my two venn diagrams that capture what i think is the case.

the first venn diagram is assuming that the 7 who sang and danced were included in the number of those who sang and those who danced.

the second venn diagram is assuming that the 7 who sang and danced were not included in the number of those who sang and those who danced.



neither of these two options will get you a total of 35 students.

you need to go back and check again what they are asking you to do.


Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Your post does not contain a question....

18 sang and 7 sang and danced --> 11 sang but did not dance.
19 danced and 7 sang and danced --> 12 danced but did not sing.

So 12 danced only; 11 sang only, and 7 did both.

That makes a total of 30 who did one or the other; so 35-30=5 did neither.

Conclusion:
danced: 12
sang: 11
both: 7
neither: 5
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

Having problem like this, first step is to check if the data is consistent.


So, we check how many people are engaged/involved in the described activities.


For it, we calculate the number of those, who are involved in any of singing or dancing.


Their number is  18 + 19 - 7 = 30.


It means that of the group of 35 people, 5 perform some other activities other than singing or dancing.


Now I can answer the problem's questions.



(a)  To find how many sang only, subtract from singing those who involved in both singing and dancing

             18 - 7 = 11 people sang only.    ANSWER



(b)  To find how many danced only, subtract from dancing those who involved in both singing and dancing

             19 - 7 = 12 people danced only.    ANSWER



(c)  The number of those who neither sang or danced is  35 - 30 = 5.    ANSWER

Solved anf thoroughly explained.

All question are answered.



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