A sports club found that 100 of its members played at least
one of football, tennis or badminton. Thirty-nine played football, 31
played tennis and 51 played badminton. Of these, 9 played both football
and tennis, 8 played both tennis and badminton and 10 played both
football and badminton. How many played just one sport?
Well, let's break it down! We know that 39 people played football, 31 people played tennis, and 51 people played badminton. Of these, 9 played both football and tennis, 8 played both tennis and badminton, and 10 played both football and badminton.
Now let's do some clown math! First, we need to find out how many people played all three sports. To do this, we can add up the overlapping numbers: 9 (football and tennis) + 8 (tennis and badminton) + 10 (football and badminton) = 27.
Next, let's find out how many people played only one sport. To do this, we subtract the sum of people who played multiple sports from the total number of people who played at least one sport. 100 - 27 = 73.
So, there were 73 people who played just one of the three sports.
To find out how many members of the sports club played just one sport, we need to subtract the number of members who played multiple sports from the total number of members who played at least one sport.
Let's break it down step by step:
1. First, we determine the number of members who played multiple sports.
- We know that 9 played both football and tennis.
- We also know that 8 played both tennis and badminton.
- Additionally, 10 played both football and badminton.
To find the number of members who played multiple sports, we can add these numbers together:
9 + 8 + 10 = 27.
2. Next, we find the total number of members who played at least one sport.
- We know that 100 members played at least one sport.
- So, if 27 played multiple sports, the remaining must have played just one sport:
100 - 27 = 73.
Therefore, 73 members of the sports club played just one sport.
To find the number of members who played just one sport, we need to subtract the number of members who played multiple sports from the total number of members who played at least one sport.
Let's assign variables:
- F: Number of members who played football
- T: Number of members who played tennis
- B: Number of members who played badminton
We are given the following information:
- F = 39
- T = 31
- B = 51
- F ∩ T = 9 (Played both football and tennis)
- T ∩ B = 8 (Played both tennis and badminton)
- F ∩ B = 10 (Played both football and badminton)
Using this information, we can calculate the number of members who played just one sport:
Number of members who played just one sport = Total - (F ∩ T ∩ B) - 2(F ∩ T ∩ B)
Total = F + T + B - (F ∩ T) - (T ∩ B) - (F ∩ B) + (F ∩ T ∩ B)
Total = 39 + 31 + 51 - 9 - 8 - 10 + (F ∩ T ∩ B)
Total = 144
Number of members who played just one sport = 144 - (F ∩ T ∩ B) - 2(F ∩ T ∩ B)
Number of members who played just one sport = 144 - 9 - 2(9)
Number of members who played just one sport = 144 - 9 - 18
Number of members who played just one sport = 117
Therefore, 117 members played just one sport.
Venn diagram, let x be the number of people playing all 3 sports
working from the inside out ...
playing both football and tennis but not badminton = 9-x
playing both football and badminton but not tennis = 10-x
playing both tennis and badminton but not football = 8-x
playing only football = 39 - (9-x) - (10-x) - x = 20 + x
playing only tennis = 31 -(9-x) - x - (8-x) = 14 + x
playing only badminton = .....
sum of all the parts = 100, this will give you x
find all the 3 "playing only ..." parts, then add them up