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At a certain school, there are 86 girls in Grade 9
Their sport preferences are indicated below:
  • 26 girls play rugby.
  • 37 girls play basketball.
  • 14 girls play both rugby and basketball.
  • 37 girls do not play rugby or basketball.
The following Venn diagram represents the
information above, but is incomplete. Give the
values of , and .

Ask by Stewart Pierce. in South Africa
Jan 24,2025

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, , , .

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Bonus Knowledge

To find the values of and in the Venn diagram:
  1. First, calculate the number of girls who play only rugby:
    Total playing rugby = 26
    Playing both rugby and basketball = 14
    So, girls playing only rugby, .
  2. Next, calculate the number of girls who play only basketball:
    Total playing basketball = 37
    Playing both rugby and basketball = 14
    So, girls playing only basketball, .
  3. For the girls who play both sports:
    From the problem, we know that .
  4. Finally, calculate the number of girls who play neither sport:
    Total girls = 86
    Girls playing rugby or basketball = Girls playing only rugby + Girls playing only basketball + Girls playing both + Girls playing neither
    We have 12 (rugby) + 23 (basketball) + 14 (both) + (neither) = 49 (total playing rugby or basketball).
    Thus, the girls playing neither, .
The values are:
  • (only rugby)
  • (only basketball)
  • (both sports)
  • (neither sport)

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