Solved on Jan 09, 2024

Find the number of associates and partners assigned to a case where the daily rate for associates is $500 and for partners is$ 1400, and the total daily charge to the client is $5800.

STEP 1

Assumptions
1. The daily rate for each associate is $500.<br />2. The daily rate for each partner is$ 1400.
3. The number of associates is three times the number of partners.
4. The total daily charge for the lawyers' services is $5800.

STEP 2

Let's denote the number of partners as $p$ and the number of associates as $a$ . According to the given information, we have:
$a = 3p$

STEP 3

We need to set up an equation that represents the total daily charge using the rates for associates and partners. The equation will be:
$500a + 1400p = 5800$

STEP 4

Since we know that $a = 3p$ , we can substitute $3p$ for $a$ in the equation:
$500(3p) + 1400p = 5800$

STEP 5

Now, distribute the $500$ across the $3p$ :
$1500p + 1400p = 5800$

STEP 6

Combine like terms to simplify the equation:
$2900p = 5800$

STEP 7

Divide both sides of the equation by $2900$ to solve for $p$ :
$p = \frac{5800}{2900}$

STEP 8

Calculate the value of $p$ :
$p = 2$

STEP 9

Now that we have the number of partners, we can find the number of associates by using the relationship $a = 3p$ :
$a = 3 \times 2$

STEP 10

Calculate the number of associates:
$a = 6$
There were 6 associates assigned to the case and 2 partners assigned to the case.

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Find the number of associates and partners assigned to a case where the daily rate for associates is $500 and for partners is$ 1400, and the total daily charge to the client is $5800.

STEP 1

Assumptions
1. The daily rate for each associate is $500.<br />2. The daily rate for each partner is$ 1400.
3. The number of associates is three times the number of partners.
4. The total daily charge for the lawyers' services is $5800.

STEP 2

Let's denote the number of partners as $p$ and the number of associates as $a$ . According to the given information, we have:
$a = 3p$

STEP 3

We need to set up an equation that represents the total daily charge using the rates for associates and partners. The equation will be:
$500a + 1400p = 5800$

STEP 4

Since we know that $a = 3p$ , we can substitute $3p$ for $a$ in the equation:
$500(3p) + 1400p = 5800$

STEP 5

Now, distribute the $500$ across the $3p$ :
$1500p + 1400p = 5800$

STEP 6

Combine like terms to simplify the equation:
$2900p = 5800$

STEP 7

Divide both sides of the equation by $2900$ to solve for $p$ :
$p = \frac{5800}{2900}$

STEP 8

Calculate the value of $p$ :
$p = 2$

STEP 9

Now that we have the number of partners, we can find the number of associates by using the relationship $a = 3p$ :
$a = 3 \times 2$

STEP 10

Calculate the number of associates:
$a = 6$
There were 6 associates assigned to the case and 2 partners assigned to the case.

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Find the number of associates and partners assigned to a case where the daily rate for associates is 500andforpartnersis500 and for partners is 500andforpartnersis1400, and the total daily charge to the client is $5800.

STEP 1

STEP 2

Let's denote the number of partners as ppp and the number of associates as aaa. According to the given information, we have:a=3pa = 3pa=3p

STEP 3

We need to set up an equation that represents the total daily charge using the rates for associates and partners. The equation will be:500a+1400p=5800500a + 1400p = 5800500a+1400p=5800

STEP 4

Since we know that a=3pa = 3pa=3p, we can substitute 3p3p3p for aaa in the equation:500(3p)+1400p=5800500(3p) + 1400p = 5800500(3p)+1400p=5800

STEP 5

Now, distribute the 500500500 across the 3p3p3p:1500p+1400p=58001500p + 1400p = 58001500p+1400p=5800

STEP 6

Combine like terms to simplify the equation:2900p=58002900p = 58002900p=5800

STEP 7

Divide both sides of the equation by 290029002900 to solve for ppp:p=58002900p = \frac{5800}{2900}p=29005800​

STEP 8

Calculate the value of ppp:p=2p = 2p=2

STEP 9

Now that we have the number of partners, we can find the number of associates by using the relationship a=3pa = 3pa=3p:a=3×2a = 3 \times 2a=3×2

STEP 10

Calculate the number of associates:a=6a = 6a=6There were 6 associates assigned to the case and 2 partners assigned to the case.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the number of associates and partners assigned to a case where the daily rate for associates is $500 and for partners is$ 1400, and the total daily charge to the client is $5800.

Let's denote the number of partners as $p$ and the number of associates as $a$ . According to the given information, we have:
$a = 3p$

We need to set up an equation that represents the total daily charge using the rates for associates and partners. The equation will be:
$500a + 1400p = 5800$

Since we know that $a = 3p$ , we can substitute $3p$ for $a$ in the equation:
$500(3p) + 1400p = 5800$

Now, distribute the $500$ across the $3p$ :
$1500p + 1400p = 5800$

Combine like terms to simplify the equation:
$2900p = 5800$

Divide both sides of the equation by $2900$ to solve for $p$ :
$p = \frac{5800}{2900}$

Calculate the value of $p$ :
$p = 2$

Now that we have the number of partners, we can find the number of associates by using the relationship $a = 3p$ :
$a = 3 \times 2$

Calculate the number of associates:
$a = 6$
There were 6 associates assigned to the case and 2 partners assigned to the case.