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:
[tex]x+y=13...(1)[/tex]
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:
[tex]400x+1000y=8800[/tex]
This equation can be simplified. Dividing by 200 on both sides:
[tex]2x+5y=44...(2)[/tex]
From (1) and (2), the system of equations is:
[tex]\begin{cases}x+y={13} \\ 2x+5y={44}\end{cases}[/tex]
