Question 1127420
Peter can either have a even number or odd number of socks. 
We can think of the worst case scenario that can happen to odd number and even number of socks.


ODD NUMBER: 5 socks are different colors so the 5 socks will not be paired.
Expression for odd number: (socks - 5)1/2 = pairs
We are subtracting 5 because we want to get rid of the socks that will not be paired. 
We are multiplying by 1/2 because a sock is 1/2 of a pair. 


EVEN NUMBER: 4 socks are different colors so the 4 socks will not be paired. 
Expression for even number: (socks-4)1/2 = pairs


Finding number of socks for 11 pairs:
Odd--> (socks-5)1/2 = 7          Even--> (socks-4)1/2 = 7
socks -5 = 14                         socks - 4 = 14
socks = 19                               socks = 18

Since even number of socks is less than even, it gives us the minimum number of socks Peter needs to take to get 7 pairs. 


Thus Peter needs to take at least 18 socks to have 11 pairs of socks.