Question

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 $1000. The law firm assigned a total of 13 lawyers to the case and was able to charge the client $8800 per day for these lawyers' services. Write a system of equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case. Define the variables that you use to write the system.

Answer 1

To find the number of associates and partners assigned to a case, define x as associates and y as partners, leading to a system of equations: x + y = 13 and 400x + 1000y = 8800.

Step-by-step explanation:

To write a system of equations to determine the number of associates assigned to the case and the number of partners assigned to the case, let us define the variables. Let x be the number of associates and y be the number of partners. We have two conditions:

• The law firm assigned a total of 13 lawyers to the case, which gives us the equation x + y = 13.
• The total daily rate charged for these lawyers is $8800, with associates charged at $400 per day and partners at $1000 per day, leading to the equation 400x + 1000y = 8800.

Therefore, the system of equations is:

• x + y = 13
• 400x + 1000y = 8800

Answer 2

see below

Step-by-step explanation:

Variables:

Associate: a

Partner: p

Equations:

400a + 1000p = 8800

a + p = 13

Solve:

a + p = 13

a = 13 - p

400a + 1000p = 8800

400(13 - p) + 1000p = 8800

5200 - 400p + 1000p = 8800

5200 + 600p = 8800

5200 + 600p = 8800

600p = 3600

p = 6 partners

a = 13 - p

a = 13 - 6

a = 7 associates