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 $600 and the daily rate for each partner is $1100. The law firm assigned a total of 10 lawyers to the case and was able to charge the client $8000 per day for these lawyers' services. Determine the number of associates assigned to the case and the number of partners assigned to the case.

There were ____associates assigned to the case and ____
partners assigned to the case.

Answer 1

Answer: x = 7

Thus 7 associates and 10 partners were assigned

Explanation:

7 associates and 10 partners were assigned

Let "x" be the number of associates assigned to

case

Let "y" be the number of partners assigned to the case

The law firm assigned a total of 17 lawyers to the case

Therefore,

x + y = 17

x = 17 - y --------- eqn 1

daily rate charged to the client for each associate is $800

daily rate for each partner is $1800

They was able to charge the client $23600 per day for these lawyers' services

Therefore,

800x + 1800y = 23600 ------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

800(17 - y) + 1800y = 23600

13600 - 800y + 1800y = 23600

1000y = 23600 - 13600

1000y = 10000

Divide both sides by 1000

y = 10

Substitute y = 10 in eqn 1

x = 17 - 10

x = 7

Thus 7 associates and 10 partners were assigned