A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $400 and the daily rate for each partner is $900. The law firm designated twice as many partners as associates to the case and was able to charge the client $4400 per day for these lawyers' services. Determine the number of associates assigned to the case and the number of partners assigned to the case.
Let x be the number of associates assigned to the case.
The number of partners assigned to the case is 2x.
The total daily rate charged to the client for the associates is 400*x = 400x.
The total daily rate charged to the client for the partners is 900*2x = 1800x.
The total daily rate charged to the client is 400x + 1800x = 2200x.
We are told that the client was charged $4400 per day for these lawyers' services, so 2200x = 4400.
Dividing both sides of the equation by 2200, we get x = 2.
Therefore, the number of associates assigned to the case is 2, and the number of partners assigned to the case is 2*2 = 4. Answer: \boxed{2, 4}.