Vera orders some prints of photos that she uploaded to her computer. She orders 3 of the [tex]$5 \times 7$[/tex] prints for [tex]$\$[/tex] 0.89[tex]$ each, 12 of the $[/tex]4 \times 6[tex]$ prints for $[/tex]\[tex]$ 0.15$[/tex] each, and 1 of the [tex]$8 \times 10$[/tex] prints for [tex]$\$[/tex] 2.99[tex]$. She also orders a photo album for $[/tex]\[tex]$ 8.69$[/tex]. Vera pays taxes that are [tex]$7\%$[/tex] of the total purchase price. Her shipping charges are based on the following table:

\begin{tabular}{|c|c|c|}
\hline Amount of Purchase & Standard Shipping & Express Shipping \\
\hline up to [tex]$\$[/tex] 20[tex]$ & free & $[/tex]\[tex]$ 3.50$[/tex] \\
\hline [tex]$\$[/tex] 50[tex]$ up to $[/tex]\[tex]$ 100$[/tex] & [tex]$\$[/tex] 6.35[tex]$ & $[/tex]\[tex]$ 8.20$[/tex] \\
\hline [tex]$\$[/tex] 100[tex]$ up to $[/tex]\[tex]$ 200$[/tex] & [tex]$\$[/tex] 7.80[tex]$ & $[/tex]\[tex]$ 11.60$[/tex] \\
\hline [tex]$\$[/tex] 200[tex]$ and over & $[/tex]\[tex]$ 10.50$[/tex] & [tex]$\$[/tex] 16.45$ \\
\hline
\end{tabular}

Vera selects standard shipping and the company bills her credit card [tex]$\$[/tex] 20.78$ for the total of the online purchase. Determine if Vera has been billed correctly for her purchase.

a. Vera has been billed correctly.
b. Vera has not been charged enough for her purchase.
c. Vera has been overcharged by [tex]$\$[/tex] 1.13$ for her purchase.
d. Vera has been overcharged by [tex]$\$[/tex] 3.50$ for her purchase.

Please select the best answer from the choices provided.



Answer :

Let's break down the steps to determine if Vera has been billed correctly for her purchase.

1. Calculate the cost of each set of prints:

- For the \(5 \times 7\) prints:
[tex]\[ 3 \text{ prints} \times \[tex]$0.89 \text{ each} = \$[/tex]2.67 \][/tex]

- For the \(4 \times 6\) prints:
[tex]\[ 12 \text{ prints} \times \[tex]$0.15 \text{ each} = \$[/tex]1.80 \][/tex]

- For the \(8 \times 10\) print:
[tex]\[ 1 \text{ print} \times \[tex]$2.99 \text{ each} = \$[/tex]2.99 \][/tex]

2. Calculate the total cost of the prints and album before tax:

- Adding the costs of prints and the album:
[tex]\[ \[tex]$2.67 + \$[/tex]1.80 + \[tex]$2.99 + \$[/tex]8.69 = \$16.15 \][/tex]

3. Calculate the tax:

- Tax rate is \(7\%\):
[tex]\[ \text{Total tax} = \[tex]$16.15 \times 0.07 = \$[/tex]1.1305 \][/tex]

4. Calculate the total cost after tax:

[tex]\[ \[tex]$16.15 + \$[/tex]1.1305 = \$17.2805 \][/tex]
Rounding to two decimals (as prices in the question are in two decimals), we get:
[tex]\[ \$17.28 \][/tex]

5. Calculate the total cost including shipping:

- Since the total purchase (\[tex]$17.28) is up to \$[/tex]20, the standard shipping is free:
[tex]\[ \text{Total cost after shipping} = \$17.28 \][/tex]

6. Compare this with the billed amount:

- Vera was billed \$20.78.

7. Determine if Vera was billed correctly:

- The billed amount is higher than the calculated total cost with free shipping, which is \$17.28.
- The difference:
[tex]\[ \[tex]$20.78 - \$[/tex]17.28 = \$3.50 \][/tex]

This indicates an overcharge of \$3.50.

Therefore, Vera has been overcharged by \$3.50. The correct answer is:

d. Vera has been over charged by \$3.50 for her purchase.

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