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?
460 * .30 = 138 take Science
460 * .75 = 345 take Math
Ant.......according to your info....it should be 65 ???
Here's the Venn Diagram
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