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 $800 and the daily rate for each partner is $1800. The law firm designated twice as many partners as associates to the case and was able to charge the client $17600 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

Let a = number of associates, p = number of partners.

Then the system is
800a + 1800p = 17600 (total daily charge)
p = 2a (twice as many partners as associates)

(If you want to solve it: substitute p = 2a → 800a + 1800(2a) = 17600 → 4400a = 17600 → a = 4, p = 8.)