SOLUTION: Make a Venn Diagram from the following information to answer questions 17 through 20: 25 students played soccer 4 boys played soccer and baseball 3 girls played soccer

Question 64046:
Make a Venn Diagram from the following information to answer questions 17 through 20:

25 students played soccer
4 boys played soccer and baseball
3 girls played soccer and baseball
10 boys played baseball
4 girls played baseball
9 students played tennis
3 boys played soccer and tennis
3 girls played soccer and tennis
3 boys played baseball and tennis
1 girl played baseball and tennis
1 boy played all three sports
1 girl played all three sports
12 girls played at least one of the three sports

19. How many students played just one of the three sports?
a)1
b)20
c)13
d)7
e)15
f) 5
20. How many girls played only baseball?
a)7
b)2
c)3
d)4
e)10
f )1

Answer by 303795(602) (Show Source): You can put this solution on YOUR website!
Ignore student gender and tally all information as students
S = Soccer B = baseball T = Tennis
S = 25
S + B = 7
B = 14
T = 9
S + T = 6
B + T = 4
S + B + T = 2
Draw up the 3 circle Venn Diagram. Put 2 (S + B + T) in the central section.
The two sections between B and T total 4. One already has a 2 so the other section must be 2 as well.
The two sections between S and B total 7. One already has a 2 so the other must be 5.
The two sections between S and T total 6. One already has a 2 so the other must be 4.
The soccer total is 25 and the three numbers already in the soccer sections are 4, 2 and 5. So the last section in soccer is 14.
Similarly you should be able to work out the last section of baseball is 5 and the last section of tennis is 1.
Students playing only one sport = 14 + 5 + 1 = 20.
Students playing soccer but not tennis or baseball = 14.
Students playing soccer and baseball but not tennis = 5

Redraw the Venn Diagram using girl only data.
s + B = 3
B = 4
S + T = 3
B + T = 1
S + B + T = 1
The central section is 1.
The two sections between B and T total 1. One already has a 1 so the other section must be 0.
The two sections between S and B total 3. One already has a 1 so the other must be 2.
The two sections between S and T total 3. One already has a 1 so the other must be 2.
B = 4 and the three baseball sections filled in total 3 so the last baseball section must be 1.
Therefore 1 girl played baseball only.

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