Question

1. 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 $1500. the law firm assigned a total of 14 lawyers to the case and was able to charge the client $17400 per day for these lawyers services. determine the number of associates assigned to the case and the number of partners assigned to the case.

Explanation:

Step1: Define Variables

Let \( x \) be the number of associates and \( y \) be the number of partners.
We have two equations:

1. \( x + y = 14 \) (total number of lawyers)
2. \( 600x + 1500y = 17400 \) (total daily charge)

Step2: Solve the first equation for \( x \)

From \( x + y = 14 \), we get \( x = 14 - y \).

Step3: Substitute \( x \) into the second equation

Substitute \( x = 14 - y \) into \( 600x + 1500y = 17400 \):
\( 600(14 - y) + 1500y = 17400 \)
\( 8400 - 600y + 1500y = 17400 \)
\( 900y = 17400 - 8400 \)
\( 900y = 9000 \)
\( y = 10 \)

Step4: Find \( x \)

Substitute \( y = 10 \) into \( x = 14 - y \):
\( x = 14 - 10 = 4 \)

Answer:

The number of associates is 4 and the number of partners is 10.