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 $1200. The law firm assigned a total of 16 lawyers to the case and was able to charge the client $15000 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

Answer:

The system of equations representing the situation are

$600a+1200p = 15,000$

$a+p = 16$

with solutions

$p =9$

$a = 7$

Step-by-step explanation:

Let us call $a$ the number of associates and $p$ the number of partners. If each associate costs $600 and each partner costs $1200, and it cost the law firm a total of $15,000, then we have

$600a+1200p = 15,000$.

Since the law firm assigned at total of 16 lawyers, we have

$a+p = 16$.

Thus, the system of equations representing the situation are

$600a+1200p = 15,000$

$a+p = 16$

And the solution to this system is found by solving for $a$ in the second equation and substituting its value in the first equation:

$a = 16-p$

$600(16-p)+1200p = 15,000$

$9600-600p+1200p=15,000$

$9600+600p=15,000$

$600p=5400$

$\boxed{ p=9}$

We put this value into $a+p = 16$ and solve for $a:$

$a+9=16$

$\boxed{a = 7}$