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At a school, all 60 students play on at least one of three teams: Basketball, Soccer, and Mathletics. 8 students play all three sports, half the students play basketball, and the ratio of the size of the math team to the size of the basketball team to the size of the soccer team is 4:3:2 .How many students at the school play on exactly two teams?

 Jan 27, 2019
 #1
avatar+533 
+2

hint: draw a venn diagram

 Jan 27, 2019
 #4
avatar+102763 
+1

asad -  did you actually try to answer this. If you did I doubt you were sucessful.  

If you want to give people hints that is fine but if you have not fully answered the question first I think you should also admit that.

 

I know in the past I have had people who have given me hints when they do not know how to do it themselves.

I have assumed that they do know how to do it and it can be very frustrating.

 

If they had admitted that they did not know but they were just trying to brainstorm with me then that would have been really good.

Melody  Jan 28, 2019
 #2
avatar+5645 
+1

xxxxxx

.
 Jan 28, 2019
edited by Rom  Jan 28, 2019
 #3
avatar+102763 
+3

Here are my thoughts - I did get a different answer from you Rom :/

 

How many students at the school play on exactly two teams?

At a school, all 60 students play on at least one of three teams: Basketball, Soccer, and Mathletics.

8 students play all three sports,       So 8 can be put where all the circles overlap.

half the students play basketball,      So 30 do basketball.  That is why I put 30 in a box for basketball.

maths:basketball:soccer    is 4:3:2 . 

 

mathsbasketballsoccer 
4324+3+2=9
4030 (we know that already)   2040+30+20=90
    

 

So we have ..  

 

 

 

From the Venn diagram we can say

x+y+z+2(a+b+c)+3*8=90    (1)    and

x+y+z+   a+b+c   +8  =60    (2)

subtract

a+b+c+2+8 = 30

a+b+c = 14

 

So I think that 14 students do exactly 2 sports.

 Jan 28, 2019
 #6
avatar+102372 
+1

Very nice, Melody!!!!

 

I didn't see this one, at all....!!!!

 

cool cool cool

CPhill  Jan 28, 2019
 #5
avatar+28125 
+4

I'm with Melody on this:

 

 Jan 28, 2019
 #7
avatar+102763 
+1

Thanks Chris and Alan. 

 Jan 29, 2019

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