We can set up this problem using a system of equations.

Let:

• $x$ be the number of partners assigned to the case.
• Since there are 3 times as many associates as partners, the number of associates will be $3x$.

The law firm charges $500 per day for each associate and $1400 per day for each partner. Therefore, the total daily charge to the client is given by:

$500(3x) + 1400(x) = 5800$

Now let's solve this equation:

1. Distribute the values: $1500x + 1400x = 5800$

2. Combine like terms: $2900x = 5800$

3. Solve for $x$: $x = \frac{5800}{2900} = 2$

So, there are 2 partners. Since the number of associates is 3 times the number of partners, the number of associates is:

$3 \times 2 = 6$

Final Answer:

• Number of associates assigned to the case: 6
• Number of partners assigned to the case: 2

Would you like further details on how this solution was reached or have any questions?

Here are some related questions for you:

1. How would the total charge change if the daily rate for associates were $600 instead of $500?
2. What would happen to the number of partners and associates if the total charge per day was $7000 instead of $5800?
3. How could we use this same type of system of equations to model a different scenario with multiple types of workers?
4. What would the solution be if the number of associates was twice the number of partners instead of three times?
5. How can the firm adjust the rates of the associates or partners to increase the daily charge to the client without changing the number of employees?

Tip: When solving word problems with multiple variables, always clearly define each variable and translate the problem into mathematical expressions or equations.