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[tex]$ \\
\hline
\end{tabular}

Vera selects standard shipping, and the company bills her credit card $[/tex]\[tex]$ 20.78$[/tex] 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]$\$[/tex] 1.13[tex]$ for her purchase.
d. Vera has been overcharged by $[/tex]\[tex]$ 3.50$[/tex] for her purchase.

Please select the best answer from the choices provided.



Answer :

Let's break down the cost of Vera's purchase in detail:

1. Cost of each type of print:
- For the 3 prints of [tex]$5 \times 7$[/tex] at [tex]$0.89 each: \[ 3 \times 0.89 = 2.67 \, \text{dollars} \] - For the 12 prints of $[/tex]4 \times 6[tex]$ at $[/tex]0.15 each:
[tex]\[ 12 \times 0.15 = 1.80 \, \text{dollars} \][/tex]
- For the 1 print of [tex]$8 \times 10$[/tex] at [tex]$2.99: \[ 1 \times 2.99 = 2.99 \, \text{dollars} \] 2. Cost of the photo album: \[ 8.69 \, \text{dollars} \] 3. Subtotal (sum of all items purchased): \[ 2.67 + 1.80 + 2.99 + 8.69 = 16.15 \, \text{dollars} \] 4. Tax calculation (7% of the subtotal): \[ 16.15 \times 0.07 = 1.1305 \approx 1.13 \, \text{dollars} \] 5. Total before shipping (subtotal + tax): \[ 16.15 + 1.13 = 17.28 \, \text{dollars} \] 6. Shipping charges based on the table: - Since Vera's total before shipping is $[/tex]17.28, which is less than [tex]$20, she qualifies for free standard shipping. 7. Final total cost (total before shipping + shipping): \[ 17.28 + 0 = 17.28 \, \text{dollars} \] Given that Vera was billed $[/tex]20.78:
[tex]\[ \text{Billed amount} - \text{Calculated amount} = 20.78 - 17.28 = 3.50 \, \text{dollars} \][/tex]

Thus, Vera has been overcharged by [tex]$3.50. Therefore, the best answer is: d. Vera has been overcharged by $[/tex]3.50 for her purchase.