First: the quotient of A divided by B is 0.375, and the sum of A and B is 66. What are A and B?

B number =66/( 1+0.375)=48.

Quantity =48*0.375= 18

Several students got together and shook hands with each other 45 times * * * How many people were there?

Everyone shakes hands with others, so the number of people * (number-1)=45, because they don't shake hands with themselves, that is, 10*9=45, so there are 10 people.