Syed took out a cash advance of d dollars from a financing company. The company deducts a fee of `1/3` of the original advanced amount long with a wire transfer fee of $30.00. Which of the following represents the final advanced amount that Syed receives after all applied fees, in dollars?

Options

A. `1/3d-30`
B. `1/3(d-30)`
C. `2/3(d-30)`
D. `2/3d-30`

Answer

To find the final amount that Syed receives after all the fees are deducted, we can follow these steps:

### Step 1: Identify the original amount
Let the original cash advance amount be denoted as \( d \) dollars.

### Step 2: Calculate the deduction from the advance
The company deducts a fee of \( \frac{1}{3} \) of the original amount. Therefore, the amount deducted is:
\[ \text{Deduction} = \frac{1}{3}d \]

### Step 3: Calculate the amount left after the deduction
After the deduction, the amount Syed has left is:
\[ \text{Amount after deduction} = d - \frac{1}{3}d \]
To simplify this, we can write:
\[ d - \frac{1}{3}d = \frac{3}{3}d - \frac{1}{3}d = \frac{2}{3}d \]

### Step 4: Subtract the wire transfer fee
In addition to the deduction, there is a wire transfer fee of $30. Thus, the final amount Syed receives after all deductions is:
\[ \text{Final amount} = \frac{2}{3}d - 30 \]

### Conclusion
The final advanced amount that Syed receives after all applied fees is:
\[ \frac{2}{3}d - 30 \]