SOLUTION: In a class of 32 pupils: 5 pupils live in New Town, travel to school by bus and eat school dinners. 3 pupils live in New Town, travel to school by bus but do not eat school dinne

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Question 941042: In a class of 32 pupils:
5 pupils live in New Town, travel to school by bus and eat school dinners.
3 pupils live in New Town, travel to school by bus but do not eat school dinner.s
9 pupils do not live in New Town, do not travel to school by bus and do not eat school dinners.
11 pupils live in New Town and have school dinners.
16 pupils live in New Town.
9 pupils travel by bus and eat school dinners.
13 pupils travel by bus.
How many pupils eat school dinners?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I do this with a Venn diagram, which is 3 intersecting
circles. When you draw them, you create 7 regions
including the center which is the intersection of
all 3 circles
------------------------
I label them:
N: live in Newtown
B: travel by bus
D: eat school dinners
---------------------
(1)
5 pupils live in New Town, travel to school by bus and eat school dinners.
That is the intersection of the 3 circles label it +5+
(2)
3 pupils live in New Town, travel to school by bus but do not eat school dinners
Label that region +3+
(3)
9 pupils do not live in New Town, do not travel to school by bus and do not eat school dinners.
This is outside all 3 circles. Put a +9+ outside them
(4)
11 pupils live in New Town and have school dinners.
This is the intersection of N and D. Add +6+ to the +5+ in the center, and
put it in the other common region to N and D
(5)
16 pupils live in New Town.
Just write +N+=+16+ for the label for circle N
(6)
9 pupils travel by bus and eat school dinners.
Add +4+ to the +5+ in the center and put it in the other
region common to B and D
(7)
13 pupils travel by bus.
Just write +B+=+13+ for the label for circle B
-----------------------------------------
Now you have to figure out values for the unknown regions
Pupils who ONLY live in Newtown = 2
Pupils who ONLY ride the bus = 1
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To figure out those who only eat school dinners:
+32+=+9+%2B+16+%2B+5+%2B+x+
+x+=+2+
2 pupils ONLY eat school dinners
---------------
Those who eat school dinners:
+6+%2B+5+%2B+4+%2B+2+=+17+
17 pupils eat school dinners
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Hope you can follow this by drawing your
own Venn diagram