Glenda makes an online purchase of 4 picture frames for [tex][tex]$\$[/tex] 12.95[tex]$[/tex] each and 4 mats for [tex]$[/tex]\[tex]$ 5.89$[/tex][/tex] each. The site says that taxes paid by the customer are [tex][tex]$6.5\%$[/tex][/tex] of the total purchase price. 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]$\$[/tex] 50[tex]$[/tex] & [tex]$[/tex]\[tex]$ 5.10$[/tex][/tex] & [tex][tex]$\$[/tex] 7.00[tex]$[/tex] \\
\hline
[tex]$[/tex]\[tex]$ 50$[/tex][/tex] up to [tex][tex]$\$[/tex] 100[tex]$[/tex] & [tex]$[/tex]\[tex]$ 6.35$[/tex][/tex] & [tex][tex]$\$[/tex] 8.20[tex]$[/tex] \\
\hline
[tex]$[/tex]\[tex]$ 100$[/tex][/tex] up to [tex][tex]$\$[/tex] 200[tex]$[/tex] & [tex]$[/tex]\[tex]$ 7.80$[/tex][/tex] & [tex][tex]$\$[/tex] 11.60[tex]$[/tex] \\
\hline
[tex]$[/tex]\[tex]$ 200$[/tex][/tex] and over & [tex][tex]$\$[/tex] 10.50[tex]$[/tex] & [tex]$[/tex]\[tex]$ 16.45$[/tex][/tex] \\
\hline
\end{tabular}

Glenda selects express shipping for her purchase and the company bills her credit card [tex][tex]$\$[/tex] 91.86[tex]$[/tex] for the total of the online purchase. Determine if Glenda has been billed correctly for her purchase.

A. Glenda has been billed correctly.
B. Glenda has not been charged enough for her purchase.
C. Glenda has been overcharged by [tex]$[/tex]\[tex]$ 3.40$[/tex][/tex] for her purchase.
D. Glenda has been overcharged by [tex][tex]$\$[/tex] 3.80$[/tex] for her purchase.



Answer :

Let's work through the purchase step-by-step to determine if Glenda has been billed correctly. Here are the key items to consider:

1. Cost of Picture Frames:
- Glenda buys 4 picture frames.
- Each frame costs \[tex]$12.95. - Total cost for frames = \( 4 \times 12.95 = 51.80 \). 2. Cost of Mats: - Glenda buys 4 mats. - Each mat costs \$[/tex]5.89.
- Total cost for mats = [tex]\( 4 \times 5.89 = 23.56 \)[/tex].

3. Total Purchase Price Before Tax:
- Total cost = cost of frames + cost of mats
- Total cost = [tex]\( 51.80 + 23.56 = 75.36 \)[/tex].

4. Sales Tax:
- Sales tax rate is 6.5%.
- Sales tax = [tex]\( 0.065 \times 75.36 = 4.90 \)[/tex].

5. Shipping Charges:
- According to the table, for a purchase amount between \[tex]$50 and \$[/tex]100, express shipping is \[tex]$8.20. - Shipping charges = \$[/tex]8.20.

6. Total Cost Including Tax and Shipping:
- Total cost including tax and shipping = total purchase price before tax + sales tax + shipping charges
- Total cost = [tex]\( 75.36 + 4.90 + 8.20 = 88.46 \)[/tex].

7. Comparing with Billed Amount:
- The company billed Glenda \[tex]$91.86. - Difference between the billed amount and the total calculated cost = \( 91.86 - 88.46 = 3.40 \). Since the difference calculated confirms the billing discrepancy, we conclude: c. Glenda has been over charged by \$[/tex]3.40 for her purchase.