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.

The number of associates = 6

The number of partners = 4

Step-by-step explanation:

let the number of associates = x

let the number of partners = y

The law firm assigned a total of 10 lawyers

∴ x + y = 10

∴ y = 10 - x ⇒ (1)

$8000 per day charged for these lawyers, The daily rate charged to the client for each associate is $600 and the daily rate for each partner is $1100.

∴ 600x + 1100 y = 8000 ⇒ (2)

Solve (1) and (2) by substitute from (1) at (2)

600 x + 1100 (10 - x) = 8000

solve for x:

600 x + 11000 - 1100 x = 8000

-500 x = - 3000

x = - 3000/-500 = 6

At (1) to find y

y = 10 - 6 = 4

So,

The number of associates = 6

And the number of partners = 4