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 $1700. The law firm assigned a total of 14 lawyers to the case and was able to charge the client $19300 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

To determine the number of associates and partners assigned to a case, we can set up a system of equations using the given information.

By solving the system, we find that there are 5 associates and 9 partners assigned to the case.

Step-by-step explanation:

Let the number of associates assigned to the case be A and the number of partners assigned to the case be P.

The daily rate charged for each associate is $800, so the total cost for all the associates would be 800A.

The daily rate charged for each partner is $1700, so the total cost for all the partners would be 1700P.

The total number of lawyers assigned to the case is 14, so we have the equation:

A + P = 14.

The total cost charged to the client is $19300 per day, so we have the equation:

800A + 1700P = 19300.

Now we can solve the system of equations to find the values of A and P.

Multiplying the first equation by -800, we get -800A - 800P

= -11200.

Adding this equation to the second equation, we eliminate A and get -800P + 1700P

= -11200 + 19300.

Simplifying, we find 900P = 8100.

Dividing both sides by 900, we find P = 9.

Substituting this value of P back into the first equation, we find A + 9 = 14.

So A = 14 - 9

= 5.

Therefore, there are 5 associates assigned to the case and 9 partners assigned to the case.