There are 250 students taking band, chorus,

Question

There are 250 students taking band, chorus, or both. If there are 180 students taking band and 60 students in both band and chorus, how many students are only in chorus?

 

im so confused on getting the answer

Answer 1

 

There are 250 total students.

 

180 take band.

60 take band and chorus .... that is the intersection of the 2 groups.

 

A venn diagram will help with this.

 

   ___________________________

  |             BAND  ONLY           |

  |                                              |

  |      180 - 60 = 120               |

  |                        _____________|_______________                     

  |                       |   BAND &    |     CHORUS    |

  |                       |  CHORUS    |        ONLY      |

  |                       |                     |                         |

  |                       |        60        |                         |

  |____________ |_ _ _ _ _ _ _ _ |                         |

                          |                                                |

                          |   250 - 180 = 70                    |

                          |____________________________|

 

 

The sum of the 3 regions is 250.

 

120 take band only.

  60 take both band and chorus

  70 take chorus only

-----

250 total

 

 

Answer 2

If there are 180 students taking band and 60 students in both band and chorus, how many students are only in chorus?

 

I believe that the underlined fact above includes all students who take band (some of whom also take chorus). That means that 120 take band ONLY.  In a Venn diagram with circles B and C partially overlapping, 60 is the count in the overlapping region, 120 is the count in the Band-only remainder of circle B, and therefore, to get to a total 250, there must be 70 in the Chorus-only part of circle C.