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 $400 and the daily rate for each partner is $1200. The law firm assigned a total of 5 lawyers to the case and was able to charge the client $3600 per day for these lawyers' services. Graphically solve a system of equations in order to determine the number of associates assigned to the case, x, commax, and the number partners assigned to the case, yy.

Answer 1

Let's assign variables to represent the number of associates and partners.
Let x represent the number of associates assigned to the case.
Let y represent the number of partners assigned to the case.

We can create two equations based on the given information:
1) The total number of lawyers assigned is 5. So, we have: x + y = 5. (Equation 1)
2) The total daily rate charged to the client is $3600. So, we have: (400 * x) + (1200 * y) = 3600. (Equation 2)

To solve this system of equations graphically, we can plot the lines represented by each equation on a graph.

First, let's rearrange Equation 1 to solve for y:
y = 5 - x.

Now, let's plot this equation on a graph.
Using the x-axis to represent the number of associates (x) and the y-axis to represent the number of partners (y), we can plot the following points:
(x, y) => (0, 5), (1, 4), (2, 3), (3, 2), (4, 1), (5, 0).

The graph will be a straight line passing through these points.

Next, let's rearrange Equation 2 to solve for y:
(1200 * y) = 3600 - (400 * x)
y = (3600 - 400 * x) / 1200
y = (36000 - 400 * x) / 1200
y = (30 - x/3).

Now, let's plot this equation on the same graph.

Using the x-axis to represent the number of associates (x) and the y-axis to represent the number of partners (y), we can plot the following points:
(x, y) => (0, 30), (1, 29), (2, 28), (3, 27), (4, 26), (5, 25).

The graph will be a straight line passing through these points.

By visually examining the graph, we can see that the lines representing the two equations intersect at a single point: (x, y) => (3, 2).

Therefore, the number of associates assigned to the case is 3, and the number of partners assigned to the case is 2.