SOLUTION: . Heather surveyed 30 members of her outdoor club (OC) and found that 18 Alpine ski tour (A) and 15 of these members also skate ski (S). Five members did not ski tour nor do they

Algebra ->  Subset -> SOLUTION: . Heather surveyed 30 members of her outdoor club (OC) and found that 18 Alpine ski tour (A) and 15 of these members also skate ski (S). Five members did not ski tour nor do they       Log On


   

Question 1043375: . Heather surveyed 30 members of her outdoor club (OC) and found that 18 Alpine ski tour (A) and
15 of these members also skate ski (S). Five members did not ski tour nor do they skate ski. Write
out formulas using set notation and calculate the following:
a) Number of participants who Alpine tour ski or Skate ski.
___________________________________________________________________________
b) Number of participants who Alpine tour ski and Skate ski.
___________________________________________________________________________
c) Number of participants who only Alpine tour ski.
___________________________________________________________________________
d) Number of participants who only Skate Ski.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Heather surveyed 30 members of her outdoor club (OC) and found that 18 Alpine ski tour (A) and 15 of these members also skate ski (S). Five members did not ski tour nor do they skate ski.
Write out formulas using set notation and calculate the following:
Draw a rectangle with intersecting A and S circles
Put 15 in the intersection of A and S
Put 18-15 = 3 in A but not in the intersection
Put 5 in the rectangle but not in either A or S
Put "x" in S but not in the intersection
Solve for "x"::
18 + x + 5 = 30
x = 7
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a) Number of participants who Alpine tour ski or Skate ski.
(A or S) = A + S - (A and S)
A or S = 18 + 22 -15 = 25
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b) Number of participants who Alpine tour ski and Skate ski.
A and S = A + S - (A or S)
A and S = 18 + 22 - 25 = 15
___________________________________________________________________________
c) Number of participants who only Alpine tour ski.
A- (A and S) = 18-15 = 3
___________________________________________________________________________
d) Number of participants who only Skate Ski.
S - (A and S) = 22-15 = 7
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Cheers,
Stan H.
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