Mr.Hash bough some plates at a a yard sale. After arriving home he found that 2/3 of the plates were chipped, 1/2 were cracked, 1/4 were both chipped and cracked. Only 2 plates were w/o chips or cracks. How many plates did he buy in all?

Answer 1

Suppose there were p plates. If you count both the ships and the cracks, then you count chipped&cracked twice.

p - 2p/3 - p/2 + p/4 = 2

12p - 8p - 6p + 3p = 24
p = 24

So, 16 were chipped
12 were cracked
6 both
2 undamaged

Answer 2

36