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 $1500. The law firm designated 3 times as many partners as associates to the case and was able to charge the client $14700 per day for these lawyers' services. Determine the number of associates assigned to the case and the number of partners assigned to the case.

The number of associates assigned to the case was 3 and the number of partners assigned to the case was 9.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Daily rate to the client for each associate (y) = US$ 400

Daily rate to the client for each partner (x) = US$ 1,500

3y = x

Lawyers' services per day charged to the client = US$ 14,700

2. Determine the number of associates assigned to the case and the number of partners assigned to the case.

3y = x

1,500x + 400y = 14,700

Replacing x in the 1st equation

1,500 (3y) + 400y = 14,700

4,500y + 400y = 14,700

4,900y = 14,700

y = 3 ⇒ x = 9

The number of associates assigned to the case was 3 and the number of partners assigned to the case was 9.