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Music High school

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by sam2304 » Sat Jan 07, 2012 6:01 pm
All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students
are in only one group. There are 119 students in the band. If 50 percent of the students are in the band only,
how many students are in the orchestra only?
A.30
B.51
C.60
D.85
E.119
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by mj78ind » Sat Jan 07, 2012 8:04 pm
Say x = Number of people in band only
y = Number in both band and orchestra
z = Number in Orchestra only

As per the question,

(x+y)/(x+y+z) = 0.8 ----- (1)

x+y = 119 ------- (2)

x = (x+y+z)/2 ------- (3)

These equations can be solved for z = 51. (Three equations three unknowns).

Hence answer is B
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