```Question 292918
A survey of fruit tree growers showed the following
75 grew raspberries
40 grew blueberries
27 grew strawberries
11 grew both raspberries and blueberries
10 grew both raspberries and strawberries
14 grew both blueberries and strawberries
4 grew all three types
9 grew none of these three
Create a venn diagram to relect
a) how many grew only raspberries?
b) how many grew both strawberries and raspberries, but not blueberries?
c) how many grew only strawberries?
d) how many grew none of these three or only blueberries?
e) how many fruit tree growers were surveyed?

3 overlapping circles (R and B and S), 8 areas (RO, BO, SO, RBO, RSO, BSO, RBS, NRBS)
circle R for raspberries, R only or RO just raspberries
circle B for blueberries, B only or BO just blueberries
circle S for strawberries S only or SO just for strawberries
RB both raspberries and blueberries, RBO just raspberries and blueberries
RS both raspberries and strawberries, RSO just raspberries and strawberries
BS both blueberries and strawberries, BSO just blueberries and strawberries
RBS rasberries, blueberries, and strawberries
NRBS is none of the 3 types
R = RO + RBO + RSO + RBS = 75
B = BO + RBO + BSO + RBS = 40
S = SO + RSO + BSO + RBS = 27
RBS = 4 (all 3 types)
RB = RBO + RBS = 11 = RBO + 4 --> RBO = 7 (not strawberries)
RS = RSO + RBS = 10 = RSO + 4 --> RSO = 6 (not blueberries)
BS = BSO + RBS = 14 = BSO + 4 --> BSO = 10 (not raspberries)
R = RO + RBO + RSO + RBS = 75 = RO + 7 + 6 + 4 = RO + 17 --> RO = 58 (raspberries only)
B = BO + RBO + BSO + RBS = 40 = BO + 7 + 10 + 4 = BO + 21 --> BO = 19 (blueberries only)
S = SO + RSO + BSO + RBS = 27 = SO + 6 + 10 + 4 = SO + 20 --> SO = 7 (strawberries only)
8 areas --> RO = 58, BO = 19, SO = 7, RBO = 7, RSO = 6, BSO = 10, RBS = 4, NRBS = 9
total fruit tree growers surveyed is sum of all 8 areas or 58 + 19 + 7 + 7 + 6 + 10 + 4 + 9 = 111 + 9 = 120
none of the 3 types or only blueberries --> 9 + 19 = 28

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