I need help with this question please

Question

Fifth graders vote to determine where they want to go on a field trip. One third of the fifth graders want to go bowling two sixths of the fifth graders want to go to the zoo one sixth of the fifth graders want to go to the museum sixteen students want to do activities at the town park how many fifth graders. It's to determine where they want to go on the field trip ?

Answer 1

Let x = number of fifth graders

 

   Bowling   +     Zoo           +        Museum       +      Park         =     All

  (1/3)x      +  (2/6)x          +         (1/6)x         +      16           =    x

 

    2x         +     2x             +           x               +     96            =   6x     [multiply all by LCD=6]

 

5x + 96 = 6x

     96 = x                     [subtract 5x from both sides]

 

There are 96 fifth graders.

 

Checking (very important):

  Is    (1/3)96 + (2/6)96 +(1/6)96 +16  =  96   ?

           32      +    32      +  16      + 16 = 96   ?

                      96 = 96   ?yes