Let x be the number of associates designated.
Let y be the number of partners designated.
If there are a total of 13 lawyers assigned to the case, then this represents the sum of associates and partners:
Additionally, we know that the daily rate charged to the client for each associate is $400 and the daily rate for each partner is $1000. Then, the daily rate for all associates is 400x and the daily rate for all partners is 1000y. Knowing that the total daily charge to the client is $8800, then:
This equation can be simplified. Dividing by 200 on both sides:
From (1) and (2), the system of equations is: