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?

Equation:

Total   =   Band Only   +   Orchestra Only    +    Both

Band Only     +     Orchestra Only      =       80%

Band  Only     =       50%

Orchestra Only      =        30%

Therefore:

Band     =    100%      -      Orchestra Only  30%    =     70%

70% of total students   =      119

Total students        =         170

Number of Students in Orchestra Only:

= ===>    30%   of    170    =     51

Solution for what is 30% of 170:  

170 / x     =     100 / 30

(170 / x)  * x  =   (100 / 30)  * x       (we multiply both sides of the equation by x)

170    =     3.33333333333 *  x        (we divide both sides of the equation by )(3.33333333333)    to get    x

170 / 3.33333333333          =          x  

51         =          x  

x       =           51

now we have:

30% of    170    =       51

Therefore your,  Answer is  > 51 students is in the Orchestra only.

Hope that helps                                          : )

step-by-step explanation: