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All of the students of Music High School are in the band, [#permalink]

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24 Aug 2008, 22:15

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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?

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? 30 51 60 85 119

not sure i got it...how the number in a group can be with 80% or 50% or 30% or 20%?

band = b orchestra = o band & orchestra = oc total = b+o - oc

if 50% are only in the band then total in band = 80% oc = 30% c = 20%

so 80% of total = 119 total = 140 c = 31 or 30 A.
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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? 30 51 60 85 119

B = Band O = Orchestra T = Total

Only Band = 0.5T Either Band or Orchestra but not both = 0.8T Hence, Only Orchestra = 0.3T Also, both is 1 - 0.8T = 0.2T

Given: % of students in one group only = 80% ---- 1. Therefore % of students in both groups = 100 - 80 = 20% -----2. Also given: % of students in the band only = 50% -----3. Also given: Number of students who are in band = 119 -----4.

Band = 50% of Students and Orchestra = 30% of students [both group consists of 80% of students] Now students who are both in two groups are 20% of students.

So total Band: 50% of Students + 20% of students = 119 Students = 170.

Hence only orchestra = 30% of students = 30% of 170 = 51
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