To determine if Glenda has been billed correctly for her purchase, let's break down the costs step by step.
1. Calculate the subtotal for frames and mats:
[tex]\[
\text{Price per frame} = \$12.95 \\
\text{Quantity of frames} = 4 \\
\text{Subtotal for frames} = 4 \times 12.95 = \$51.80
\][/tex]
[tex]\[
\text{Price per mat} = \$5.89 \\
\text{Quantity of mats} = 4 \\
\text{Subtotal for mats} = 4 \times 5.89 = \$23.56
\][/tex]
[tex]\[
\text{Total subtotal} = \$51.80 + \$23.56 = \$75.36
\][/tex]
2. Calculate the tax amount based on the subtotal:
[tex]\[
\text{Tax rate} = 6.5\% \\
\text{Tax amount} = 75.36 \times 0.065 = \$4.8984 \approx \$4.90
\][/tex]
3. Calculate the total before shipping:
[tex]\[
\text{Total before shipping} = \$75.36 + \$4.90 = \$80.26
\][/tex]
4. Determine the shipping cost based on the total before shipping:
Since Glenda selected express shipping and the amount before shipping is \[tex]$80.26, we refer to the shipping table:
\[
50 < \$[/tex]80.26 \leq 100 \Rightarrow \text{Express Shipping} = \[tex]$8.20
\]
5. Calculate the final total including shipping:
\[
\text{Final total} = \$[/tex]80.26 + \[tex]$8.20 = \$[/tex]88.46
\]
6. Compare the calculated final total with the billed amount:
[tex]\[
\text{Billed amount} = \$91.86
\][/tex]
[tex]\[
\text{Difference} = \$91.86 - \$88.46 = \$3.40
\][/tex]
Given the choices:
a. Glenda has been billed correctly.
b. Glenda has not been charged enough for her purchase.
c. Glenda has been overcharged by \[tex]$3.40 for her purchase.
d. Glenda has been overcharged by \$[/tex]3.80 for her purchase.
From the calculations above, Glenda has been overcharged by \[tex]$3.40.
Hence, the correct answer is:
c. Glenda has been overcharged by \$[/tex]3.40 for her purchase.
