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.
