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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?

ant101 Dec 2, 2018

#1**+2 **

460 * .30 = 138 take Science

460 * .75 = 345 take Math

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

Here's the Venn Diagram

CPhill Dec 2, 2018

#4**+2 **

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

CPhill Dec 2, 2018