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Please guys help me please with this question please please please please ​

Please guys help me please with this question please please please please ​-example-1
User Keisha
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1 Answer

12 votes
12 votes

Answer:

x = 18

Explanation:

Given:

  • 160 total learners
  • 34 play soccer and rugby
  • 40 play soccer and hockey
  • 42 play hockey and rugby
  • 36 play soccer only
  • 72 play hockey
  • 8 play rugby only
  • 28 play none of these sports
  • x play all three sports

As "x" learners play all three sports, the Venn diagram should have three overlapping circles labelled soccer (S), rugby (R) and hockey (H).

x play all three sports: Label the area that's in S, R and H with x.

8 play rugby only: Label the area that is R only with 8.

36 play soccer only: Label the area that is S only with 36.

28 play none of these sports: Place 28 outside the three circles.

34 play soccer and rugby: Place "34 - x" in the area that's in S and R.

40 play soccer and hockey: Place "40 - x" in the area that's in S and H.

42 play hockey and rugby: Place "42 - x" in the area that's in H and R.

72 play hockey

72 is the total for all the sections of H.

⇒ H = 72 - x - (40 - x) - (42 - x)

⇒ H = 72 - x - 40 + x - 42 + x

⇒ H = x - 10

Place "x - 10" in the area that is H only.

The total number of learners is 160.

Therefore, to find x, sum the areas of the Venn diagram and equal to 160:

⇒ 36 + 8 + 28 + 34 - x + x + 40 - x + 42 - x + x - 10 = 160

⇒ 36 + 8 + 28 + 34 + 40 + 42 - 10 - x + x - x - x + x = 160

⇒ 178 - x = 160

⇒ x = 178 - 160

⇒ x = 18

Finally, substitute x = 18 into the Venn diagram.

Please guys help me please with this question please please please please ​-example-1
Please guys help me please with this question please please please please ​-example-2
User Alex Roslyakov
by
2.9k points
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