Solve System of Equations from Context

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 $900. The law firm designated twice as many partners as associates to the case and was able to charge the client $4400 per day for these lawyers' services. Determine the number of associates assigned to the case and the number of partners assigned to the case.

Answer 1

p=2a partners = twice associates assigned to the case

$4400 total charge per day

$400 per day for an associate, $900 per day for a partner's time on the case

400a + 900p = 4400

4a +9p = 44

4a +9(2a) = 44

4a +18a = 44

22a = 44

a = 44/22 = 2 associates on the case each day

p =2a = 2(2) = 4 partners on the case each day

400(2) + 900(4) = 800 + 3600 = 4400