Suppose you want to wash 5*20= 100 dishes in 20 minutes, and:

Every time Aunt Zhang washes the cup 1 min, the total number of washed tableware will increase by 9-3 = 6;

Aunt Li will increase the total number of tableware washing by 7-2=5 every 1 minute;

Now the total number of dishes to be washed has increased 134- 100=34.

It depends: 34 can be broken down into 6 and 5.

Obviously: 34 = 4*6+2*5.

So: Aunt Zhang spent 4 minutes washing cups (16 minutes washing dishes).

Aunt Li spent 2 minutes washing cups (18 minutes washing dishes).

Number of boards = 16*3+18*2 = 84.

The number of cups = 4*9+2*7 = 50.