Question

find the amount of the credit given to the business, based on the sales/refunds record for 09/24/10, after the 5.75% fee is subtracted. the total amount of credit will be $\square$. (round to the nearest cent as needed.) 09/24/10 sales $84.68 $53.84 $188.24 $495.66 $85.12 $94.11 $163.58 $250.65 $284.99 $143.87 refunds $33.59 $128.14 $54.08

Explanation:

Step1: Calculate total sales

First, sum up all the sales amounts. The sales amounts are $84.68, $188.24, $85.12, $163.58, $284.99.
\[

$$\begin{align*} \text{Total Sales} &= 84.68 + 188.24 + 85.12 + 163.58 + 284.99\\ &= (84.68 + 188.24) + (85.12 + 163.58) + 284.99\\ &= 272.92 + 248.7 + 284.99\\ &= 521.62 + 284.99\\ &= 806.61 \end{align*}$$

\]

Step2: Calculate total refunds

Next, sum up all the refund amounts. The refund amounts are $33.59, $128.14, $54.08.
\[

$$\begin{align*} \text{Total Refunds} &= 33.59 + 128.14 + 54.08\\ &= 161.73 + 54.08\\ &= 215.81 \end{align*}$$

\]

Step3: Calculate net amount before fee

The net amount before the fee is total sales minus total refunds.
\[
\text{Net Amount Before Fee} = 806.61 - 215.81 = 590.8
\]

Step4: Subtract the 5.75% fee

The fee is 5.75% of the net amount before fee, so the amount after subtracting the fee is the net amount before fee multiplied by (1 - 0.0575).
\[
\text{Credit Amount} = 590.8 \times (1 - 0.0575) = 590.8 \times 0.9425
\]
Calculate the product:
\[
590.8 \times 0.9425 = 590.8 \times 0.9 + 590.8 \times 0.04 + 590.8 \times 0.0025
\]
\[
= 531.72 + 23.632 + 1.477 = 556.829
\]
Wait, no, better to calculate directly:
\[
590.8 \times 0.9425 = 590.8 \times \frac{9425}{10000} = \frac{590.8 \times 9425}{10000}
\]
\[
590.8 \times 9425 = 590.8 \times (9000 + 400 + 25) = 590.8 \times 9000 + 590.8 \times 400 + 590.8 \times 25
\]
\[
= 5317200 + 236320 + 14770 = 5317200 + 236320 = 5553520 + 14770 = 5568290
\]
Then divide by 10000: \( \frac{5568290}{10000} = 556.829 \approx 556.83 \)

Wait, maybe I made a mistake in total sales. Wait, looking back, the sales column has two columns? Wait, the table has two sales columns? Wait, the original table:

Wait, the right table: Sales has two columns? Wait, the first column of Sales: $84.68, $188.24, $85.12, $163.58, $284.99; second column of Sales: $53.84, $495.66, $94.11, $250.65, $143.87. Oh! I missed the second sales column. So total sales is sum of both sales columns.

Let's recalculate total sales:

First sales column: 84.68, 188.24, 85.12, 163.58, 284.99

Second sales column: 53.84, 495.66, 94.11, 250.65, 143.87

So total sales:

\[

$$\begin{align*} &(84.68 + 53.84) + (188.24 + 495.66) + (85.12 + 94.11) + (163.58 + 250.65) + (284.99 + 143.87)\\ &= 138.52 + 683.9 + 179.23 + 414.23 + 428.86\\ &= (138.52 + 683.9) + (179.23 + 414.23) + 428.86\\ &= 822.42 + 593.46 + 428.86\\ &= 822.42 + 593.46 = 1415.88 + 428.86 = 1844.74 \end{align*}$$

\]

Total refunds: 33.59, 128.14, 54.08

\[
33.59 + 128.14 + 54.08 = 215.81
\]

Net amount before fee: Total sales - Total refunds = 1844.74 - 215.81 = 1628.93

Now, subtract the 5.75% fee: 1628.93 (1 - 0.0575) = 1628.93 0.9425

Calculate that:

1628.93 * 0.9425

First, 1628.93 * 0.9 = 1466.037

1628.93 * 0.04 = 65.1572

1628.93 * 0.0025 = 4.072325

Add them up: 1466.037 + 65.1572 = 1531.1942 + 4.072325 = 1535.266525 ≈ 1535.27

Wait, let's do it more accurately:

1628.93 0.9425 = 1628.93 (9425 / 10000) = (1628.93 * 9425) / 10000

Calculate 1628.93 * 9425:

First, 1628.93 * 9000 = 14660370

1628.93 * 400 = 651572

1628.93 * 25 = 40723.25

Sum: 14660370 + 651572 = 15311942 + 40723.25 = 15352665.25

Divide by 10000: 15352665.25 / 10000 = 1535.266525 ≈ 1535.27

Yes, that's correct. Because I missed the second sales column initially. So the total sales is the sum of both sales columns, then subtract refunds, then apply the (1 - 5.75%) factor.

Answer:

\boxed{1535.27}