A law firm is going to designate associates and partners to a hug new case. The daily rate of charged to the client for each associate is $500 and the daily rate for each partner is $1000. The law firm assigned a total of 8 lawyers to the case and was able to charge the client $6500 per day for these lawyers services. Determined the number of associates assigned to the case and the number of partners assigned to the case

There are 3 associates and 5 partners assigned to the case.

Step-by-step explanation:

We know that the combined cost of the unknown number of associates and partners equals $6500 per day, and that the amount of associates and partners assigned to the case equals 8, so we can derive these two equations (where a is associates and p is partners):

500a + 1000p = 6500

a + p = 8

Let's use the second one first to isolate the a ...

a + p = 8

If we subtract p from both sides of the equation we get:

a = 8 - p

Now we may use this in our original equation to solve for p

500 (8-p) + 1000p = 6500

If we simplify by distribution, we get:

4000 - 500p + 1000p = 6500

Now let's add those two p's together ...

4000 + 500p = 6500

And subtract 4000 from both sides to get:

500p = 2500

Now finally, divide both sides of the equation by 500 to get p:

p = 5

We now have the number of partners involved (5), and we know that the amount of associates plus the amount of partners assigned to the case equals 8, so we can plug the amount of partners assigned into the second formula to get a:

a + 5 = 8

And by subtracting 5 from both sides we get ...

a = 3