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# Venn Diagrams

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Problem: There are 460 people at my school. 30 percent of the people take Science, whereas 75 percent of the people take math. 65 people who take Science also take math. How many people take both math and science?

Dec 2, 2018

#1
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460 * .30 = 138 take Science

460 * .75 = 345 take Math

Ant.......according to your info....it should be 65 ???

Here's the Venn Diagram

Dec 2, 2018
#2
+878
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Thanks! So, we only need that info. But, does that go under the column both?

One more question: If they asked the number of students who didn't take any classes, what would the answer be?

ant101  Dec 2, 2018
#3
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Also, isn't 30+75=105 percent. What should we do with the 5%?

Dec 2, 2018
#4
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Yeah.... I should have labeled the "65" as "Both"

The number of students who didn't take either =

460 - (75 + 65 + 280 )  = 42

We aren't summing 75 + 30  [ remember that some of this "sum" is being "double-counted"]

We are just noting that     73/460 take only Science.....65/460 take Both and 280/460 take Math

So       [ 73 + 65 + 280 ] /  460 = 418/460   take only Math, only Science, or Both

And 42 /460 take neither

Dec 2, 2018
#5
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Thank you, CPhill!

ant101  Dec 2, 2018
#6
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OK.....hope that helped

CPhill  Dec 2, 2018