SOLUTION: in a survey 1/3 children like only mango and 25 donot like mango at all also 2/5 children like orange but 16 like none of them. then show above data in venn-diagram and find number

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Question 1083807: in a survey 1/3 children like only mango and 25 donot like mango at all also 2/5 children like orange but 16 like none of them. then show above data in venn-diagram and find number of children who like both fruit
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This is 2 interlocking circles giving you
3 distinct regions:
(1) Only like mango
(2) Like both mango and orange
(3) Only like orange
-------------------------------
They tell you that everything outside these
2 circles is +16+ children ( like none of them )
--------------------------------------------
Let +C+ = the total number of children
Area (1) Only like mango = +%28+1%2F3%29%2AC+
--------------------------------------
+25+ do not like mango.
Let +x+ = (3) Only like orange
+x+%2B+16+=+25+
+x+=+9+
---------------------------------------
+%282%2F5%29%2AC+ = like orange
+%282%2F5%29%2AC+-+9+ = area (2) Like both mango and orange
----------------------------------------------------
I have specified the 3 areas and also everything outside ( +16+ children )
so, now I can say:
+C+=+%281%2F3%29%2AC+%2B+%282%2F5%29%2AC+-+9+%2B+9+%2B+16+
+C+=+%281%2F3%29%2AC+%2B+%282%2F5%29%2AC+%2B+16+
+C+=+%285%2F15%29%2AC+%2B+%28+6%2F15+%29%2AC+%2B+16+
+15C+=+5C+%2B+6C+%2B+240+
+4C+=+240+
+C+=+60+
--------------------
(2) Like both mango and orange = +%28+2%2F5%29%2AC+-+x+
+%282%2F5%29%2AC+-+x+=+%282%2F5%29%2A60+-+9+
+%282%2F5%29%2AC+-+x+=+24+-+9+
+%282%2F5%29%2AC+-+x+=+15+
So 15 children like both fruit
----------------------------
check the answer:
+%281%2F3%29%2AC+=+%281%2F3%29%2A60+
+%281%2F3%29%2AC+=+20+ = area (1)
------------------------------
+%282%2F5%29%2AC+-+x+=+15+ = area (2)
-------------------------------
+x+=+9+ = area (3)
and
+16+ = children who like neither fruit
--------------------------------------
+20+%2B+15+%2B+9+%2B+16+=+60+
+35+%2B+25+=+60+
+60+=+60+
OK