Please note that I have never studied GCSE mathematics, so my solutions are not necessarily the “official” way of solving problems. I just solve them in a way that occurs to me.
Here’s the question:
50 people each did one activity at a sport. Some of the people went swimming. Some of the people played squash. The rest of the people used the gym. 21 of the people were female. 6 of the 8 who played squash were male. 18 of the people used the gym. 9 males went swimming
To try to get a handle on all of these numbers, I decided to lay them out into a table. Using Sw to represent swimming, Sq for squash, G for Gym, M for male, F for female, and T for Total. I have:
Sw Sq G T M 9 6 x 29 F ? 2 y 21 T ? 8 18 50
When you lay it out like that, the approach to the solution is more obvious. We are trying to find ‘y’. ‘y’ is dependent on ‘x’, so we need to find that, too.
What is the value of x? From M row, we see that:
9 + 6 + x = 29
15 + x = 29
x = 29 – 15 = 14
We can see in the Gym column that the following must hold:
x+y = 18
14 + y = 18
y = 18 – 14 = 4