At a T-shirt auction, 42 Reds United T-shirts were sold and 30 Blues T-shirts were sold. No one bought more than one T-shirt of the same type and everyone bought at least one. If 60 people participated in the auction, how many bought both T-shirts?

Solution:
Number of people who bought Reds United T-shirts = n(R) = 42

Number of people who bought Blues T-shirts = n(B) = 30

Let the number of people who bought both
T-shirts = n(R B) = x

The total number of people participating in the auction = n(R B) = 60

As everyone bought at least one T-shirt,
n(R B) = n(R) + n(B) n(R B)

x = 42 + 30 – 60

x = 12

The number of people who bought both T-shirts = n(R B) = 12

Alternatively, the question can be easily solved by Venn diagram.



It is given that everyone bought at least one T-shirt,
From the diagram, we can see that

42 x + x + 30 x = 60

x = 12