Maths

posted by .

There are 47 in a club. 18 play chess and 13 play tennis. The number who play neither is 3 times the number who play both. How many play both?

  • Maths -

    Let x = number who play both
    then 3x = number who play neither.
    C = set of people who play chess
    T = set of people who play tennis
    U = total membership of the club

    By the principle of inclusion-exclusion,
    |C∪T| = |C| + |T| - |C∩T|

    or

    |U| - |C∪T| = |U| - (|C| + |T| - |C∩T|)

    3x = 47 - (18+13-x)
    2x = 16
    x = 8 (number of members who play both)
    3x = 24 (number of members who play neither)

    Total number of players
    = |C∪T|
    = |C| + |T| - |C∩T|
    = 18 + 13 - 8
    = 23

    Check:
    |U|=|C∪T|+24
    = 23+24
    =47 OK

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. pre- algebra

    In a survery, students were asked whether they play basketball or tennis. Of 34 students, 24 play basketball and 13 students play tennis.4 students play neither. How many students play both sports?
  2. pre- algebra

    In a survery, students were asked whether they play basketball or tennis. Of 34 students, 24 play basketball and 13 students play tennis.4 students play neither. How many students play both sports?
  3. math

    in a class of 38 children,19 play tennis, 21 play squash and 10 play neither sport. (1)how many children play both sports?
  4. Maths

    The 90 members of a sports club play at least one of the games,tennis,football and volleyball. 10 play tennis and football,19 play football and volley ball,and 29 play tennis and volley ball. n people play all three games. 2n people …
  5. Maths

    The 90 members of a sport club play at least one of the games,tennis,football and volleyball. 10 play tennis and football,19 play football and volley ball,and 29 play tennis and volleyball. n people play all three games. 2n people …
  6. Math

    Class of 20 students, 13 play soccer, 8 play tennis and 2 play neither. Find how many students a) Play soccer or tennis b) Play both soccer and tennis c) Play only soccer
  7. math,

    in a class of 35 students 26 play football and play 20 long tennis, if 17 play above, many play neither.
  8. MATH

    110 MEMBER OF CLUB PLAY 1 GAME FO BA AND VO 20 PLAY FO AND BA 15 PLAY FO AND VO 26 PLAY BA AND VO x PLAY ALL 2x PLAY EAC
  9. maths

    In a class of 120 students 60 play tennis, 50 play polo,and 20 play both then how many neither play tennis nor polo?
  10. maths set

    The 79 members of a spot club play at least one of the following games Tennis, Football and Volleyball. 19 play Football & Volleyball and 29 play Tennis & Volleyball, n play all the three games. 2n people , each play only one game. …

More Similar Questions