Agroup of old ladies meet for an afternoon tea party. they bring all their cats. in all, there are 22 heads and 72 feet. how many old ladies and how many cats are in the room?

You can solve it using  a system of equations, but it's boring. I will try to describe a different, faster and more fun way.

Imagine... each guest at the tea party have four legs. Then in the room should be 22 * 4 = 88 legs. But we know there were only 72 legs.
88-72 = 16 extra legs.
So, we imagined each old lady had 4 legs and we got 16 extra legs. These extra legs we added to all the old ladies, two extra legs for each lady. Now we can find out how many old ladies were in the room.
To do this, we must divide extra legs by 2.
16/2 = 8 old ladies.
If there were 8 old ladies, then there were  22-8 = 14 cats. 

Dwould be the answer