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At Annville Junior High School, 30% of the students in the Math Club are in the Science Club, and 80% of the students in the Science Club are in the Math Club. There are 15 students in the Science Club. How many students are in the Math Club?

 Oct 21, 2017
 #1
avatar+9464 
+2

There are  15  people in the science club.

 

80% of the people in the science club are in both the science and math clubs, so...

 

number of people in both clubs  =  0.8 * 15  =  12

 

Let the number of people in math club  =  m

 

30% of the people in the math club are in both the science and math clubs,

and remember there are  12  people that are in both clubs, so...

 

0.3m  =  12

 

m  =  12 / 0.3

 

m  =  40

 Oct 21, 2017
 #2
avatar+128405 
+3

There are 15 students in the Science Club.......80%  of these are in the Math Club....

 

Note that 80%  =  4/5....so 4/5 * 15  =  60/ 5 = 12 

 

So....12 students in the Science Club are Math Club members

 

And these 12 represent 30% of the Math Club

 

Call the total members in the Math Club, M

 

So.....

 

30% of M  = 12      or, put another way

 

.30 M  = 12        divide both sides by .30

 

M  =  12 / .30  =  40 students in the Math Club

 

 

 

cool cool cool

 Oct 21, 2017
 #3
avatar+128405 
+1

Sorry, hectictar.....I didn't see that you were answering, too....smiley smiley smiley

 

 

 

cool cool cool

 Oct 21, 2017
 #4
avatar+9464 
+1

I went into hiding!!  smiley

 

Well..... I logged out before I started answering because I didn't know for sure if I could get it   smiley

hectictar  Oct 21, 2017
 #5
avatar+128405 
+1

Aha....a "stealth" answerer...........the sneakiest kind.....LOL!!!

 

 

cool cool cool

 Oct 21, 2017
 #6
avatar+9464 
+1

They'll sneak up right behind you...and suddenly....BOO!!

 

 

It  is close to Halloween, after all !!! Gotta watch out!!  laughlaugh

 Oct 21, 2017
edited by hectictar  Oct 21, 2017

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