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#1 2018-07-28 04:09:51

Strangerrr
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Registered: 2018-07-28
Posts: 7

Conditional Statements and Venn Diagrams

15. 500 people are enrolled in at least two of these three classes: art, drama, and piano.  170 are enrolled in both art and drama, 150 are enrolled in both piano and drama, and 300 are enrolled in art and piano.  How many of the 500 people are enrolled in all three?

A300
B330
C200
D120
E 90
F 60

I need help getting the right answer using the venn diagram.

D and E are incorrect.

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#2 2018-07-28 04:40:11

Strangerrr
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Registered: 2018-07-28
Posts: 7

Re: Conditional Statements and Venn Diagrams

I need help forming a Venn diagram for This question.

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#3 2018-07-28 04:41:28

Strangerrr
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Registered: 2018-07-28
Posts: 7

Re: Conditional Statements and Venn Diagrams

I know the answer is F 60 but I want how to get the answer using the diagram.

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#4 2018-07-28 04:59:30

zetafunc
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Registered: 2014-05-21
Posts: 2,213
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Re: Conditional Statements and Venn Diagrams

Draw a Venn diagram with 3 overlapping circles, labelling the four bits that overlap as A, B, C, D.

The information given in the question then allows you to form some equations for A, B, C and D. Can you see how?

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#5 2018-07-28 05:48:30

Strangerrr
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Registered: 2018-07-28
Posts: 7

Re: Conditional Statements and Venn Diagrams

Thank you
I got it now ?

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#6 2018-07-28 06:33:15

zetafunc
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Registered: 2014-05-21
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Re: Conditional Statements and Venn Diagrams

Good to hear -- welcome to the forum!

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#7 2018-07-28 16:11:31

Alg Num Theory
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Registered: 2017-11-24
Posts: 339
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Re: Conditional Statements and Venn Diagrams

Let x be the number of people enrolled in all three classes. Then:

  1. 170−x are enrolled in art and drama but not piano,

  2. 150−x are enrolled in drama and piano but not art,

  3. 300−x are enrolled in piano and art but not drama.

Now that you have split the numbers into non-overlapping groups, you can add them up:

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#8 2018-07-28 16:26:44

Strangerrr
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Registered: 2018-07-28
Posts: 7

Re: Conditional Statements and Venn Diagrams

Thank you

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