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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?

A. 30
B. 51
C. 60
D. 85
E. 11

Respuesta :

Answer:

Option B.

Step-by-step explanation:

It is given that all of the students of Music High School are in the band, the orchestra, or both.

Students only one group = 80%

Students in both groups = 100%-80% = 20%

Students in band only = 50%

Students in band = Students in band only + Students in both groups

                             = 50% + 20% = 70%

Students in orchestra only = 100% - 70% = 30%

There are 119 students in the band.

Let total number of student be x.

[tex]70\% of x=119[/tex]

[tex]\dfrac{70}{100}x=119[/tex]

[tex]0.7x=119[/tex]

[tex]x=170[/tex]

Total number of students is 170.

We know that 30% of all students are in orchestra only.

[tex]170\times \dfrac{30}{100}=51[/tex]

Therefore, the correct option is B.

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