There are 70 women in a club. Each play at least one of the following games:20 play volleyball only ‘10 play basketball only,6 play table-tennis only. 4 play all the three games and an equal number play two games only. a) Illustrate this information on a Venn diagram. b) Find the number of women who play volleyball.
Start with your Venn Diagram of the three intersecting circles. The 4 goes in the very middle, and work your numbers outwards.
What answer do you get?
To illustrate this information on a Venn diagram, we can use circles to represent each game and their intersections to show the number of women who play multiple games. Here's how to create the Venn diagram:
Step 1: Draw three overlapping circles to represent volleyball (V), basketball (B), and table tennis (T).
Step 2: Label the areas outside the circles with the numbers playing only a specific game: 20 for volleyball only (V), 10 for basketball only (B), and 6 for table tennis only (T).
Step 3: Label the overlapping regions with the number of women who play multiple games. In this case, 4 play all three games (V, B, T).
Step 4: The remaining area within the circles represents the number of women who play two games only. Since the number of women who play two games only is equal, divide this area equally and label them as x.
Step 5: Now, we can complete the Venn diagram with our given information.
To find the number of women who play volleyball, we need to add up the number of women in the volleyball-only circle (20), the number of women who play volleyball and basketball (x), and the number of women who play all three games (4). Thus, the number of women who play volleyball is 20 + x + 4.
Since we have not been given the value of x, we need additional information to determine the exact number.