Sharms wrote:Of the 84 parents who attended a meeting at a school, 35 volunteered to supervise children during the school picnic and 11 volunteered both to supervise children during the picnic and to bring refreshments to the picnic. If the number of parents who volunteered to bring refreshments was 1.5 times the number of parents who neither volunteered to supervise children during the picnic nor volunteered to bring refreshments, how many of the parents volunteered to bring refreshments?
A) 25
B) 36
C) 38,
d) 42
e) 45
The value in red (see above) reflects the intended total number of parents.
Total = Group 1 + Group 2 - Both + Neither.
The big idea with overlapping groups is the SUBTRACT THE OVERLAP.
When we count everyone in Group 1 (those who volunteer to supervise) and everyone in Group 2 (those who volunteer to bring refreshments), those in BOTH groups (those who volunteer to do both) are counted TWICE.
Thus, we SUBTRACT THE OVERLAP -- the number in both groups -- so that these people are not double-counted.
In the problem above:
Total = 84.
Group 1 = Supervise = 35.
Both = 11.
Neither = x.
Since
the number of parents who volunteered to bring refreshments was 1.5 times the number of parents who neither volunteered to supervise during the picnic nor volunteered to bring refreshments:
Group 2 = Refreshments = 1.5x.
Plugging these values into the formula, we get:
84 = 35 + 1.5x - 11 + x
84 = 24 + 2.5x
x = 60/(2.5) = 600/25 = 24.
Thus:
Refreshments = 1.5(24) = 36.
The correct answer is
B.
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