Question 644666: Please help with this, it is only one problem with several parts to it. marilyn cazayoux, financial aid director of a small private southern college surveyed the records of 100 sophomores and found the following: 49 receive government grants, 55 receive private scholarships, 43 receive aid from the college, 23 receive government grants and private scholarships, 18 receive government grants and aid from the college, 28 receive private scholarships and aid from the college, 8 receive from all 3 sources. how many of the students in the survey a) have government grants only. b) have private scholarships but not government grants, c) receive financial aid from only one of these two sources, d) receive aid from exactly 2 of these sources, e) receive no financial aid from any of the sources and f) receive no aid from college or from the government.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! marilyn cazayoux, financial aid director of a small private southern college surveyed the records of 100 sophomores and found the following: 49 receive government grants, 55 receive private scholarships, 43 receive aid from the college,
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Procedure:
Draw a Venn Diagram:
Draw a rectangle; label it U = 100
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Draw 3 intersecting circles inside the rectangle, labeling them
rgg = 49, rps= 55, rca = 43,
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Fill in numbers from the inside (intersection) of all the circles
to the outside.
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Start with 8 in the inner-most intersection.
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23 receive government grants and private scholarships,
Put 23-8 = 15 in the intersection of rgg and rps
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18 receive government grants and aid from the college,
Put 18-8 = 10 in the intersection of rgg and rcs
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28 receive private scholarships and aid from the college
Put 28-8 = 20 in the intersection of rps and rcs
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8 receive aid from all 3 sources.
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how many of the students in the survey a) have government grants only.
49-(10+15+8) = 16
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b) have private scholarships but not government grants,
55 -(15+8) = 32
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c) receive financial aid from only one of these two sources,
Ans: 12 + 16 = 28
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d) receive aid from exactly 2 of these sources,
Ans: 10 + 15 + 20 = 45
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e) receive no financial aid from any of the sources
100 - [8 + 10 + 15 + 20 + 16 + 12 + 5] = 14
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f) receive no aid from college or from the government.
Ans: 12
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Cheers,
Stan H.
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