sets problem

Question

there is a class of 50 students,awards are given for math and science.

 

36 received for either math or science

6 received both awards

2x received for math only

x received for science

 

calculate x

Answer 1

 

     _____________

    | Math             |

    |         34         |

    |              ____ |______

    |             |        |          |

    |             |  6    |          |

    |_______|___ _|          |

                  |          14      |

                  |  Science      |

                  |___________|

 

2x + (x - 6) = 36

 

3x = 42

 

x = 14

 

 

Check: 14 students get science awards.  8 students get only science awards.

 

28 students get only math awards.  34 students get math awards.

 

14 science awards + 34 math awards = 48 total awards.

 

 

36 + 2(6) = 48 total awards.

Answer 2

6+2X+X=36

3X=30

X=10