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You are making several purchases from the B-Better Electronics store. You can buy from this store online or in a physical store. You have a coupon for [tex]20\%[/tex] off that can only be used in the physical store and a [tex]\[tex]$20.00[/tex] off coupon that can only be used online. The sales tax of [tex]7.5\%[/tex] only applies to the physical store. Shipping for the online store is a flat rate of [tex]\$[/tex]8.99[/tex] or free for purchases over [tex]\[tex]$75.00[/tex]. Using the information below, determine which way of purchasing would save you the most money.

Be sure to include in your response:
- the steps you followed to complete your computations
- the choice you made regarding which way to purchase the items
- the total cost of your purchases

The prices for the items if you buy them at the B-Better Electronics store:

\begin{tabular}{|c|c|c|}
\hline Item & Quantity & Original Price \\
\hline Headphones & 1 pair & \$[/tex]14.99/ea \\
\hline DVDs & 4 DVDs & \[tex]$13.95/ea \\
\hline CDs & 2 CDs & \$[/tex]9.85/ea \\
\hline
\end{tabular}

Here are the prices for the items if you buy them from the online store:

\begin{tabular}{|l|l|l|}
\hline Item & Quantity & Original Price \\
\hline Headphones & 1 pair & \[tex]$13.50/ea \\
\hline DVDs & 4 DVDs & \$[/tex]14.99/ea \\
\hline CDs & 2 CDs & \$10.99/ea \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To determine the most cost-effective way to purchase items from B-Better Electronics, we need to calculate the final costs for both shopping methods—physically in-store and online—by considering discounts, sales tax, and shipping costs. Below is a detailed, step-by-step solution to this problem:

### Physical Store Purchase

1. Calculating Total Cost Before Discounts and Taxes:
- Headphones: [tex]\(1 \times \$14.99 = \$14.99\)[/tex]
- DVDs: [tex]\(4 \times \$13.95 = \$55.80\)[/tex]
- CDs: [tex]\(2 \times \$9.85 = \$19.70\)[/tex]

Summing these amounts gives us the total cost:
[tex]\[ \$14.99 + \$55.80 + \$19.70 = \$90.49 \][/tex]

2. Applying 20% Discount:
- Discount amount: [tex]\(0.20 \times \$90.49 = \$18.098\)[/tex]

Subtract the discount from the total cost:
[tex]\[ \$90.49 - \$18.098 = \$72.392 \][/tex]

3. Applying Sales Tax of 7.5%:
- Sales tax: [tex]\(0.075 \times \$72.392 = \$5.4294\)[/tex]

Add the sales tax to the discounted price:
[tex]\[ \$72.392 + \$5.4294 = \$77.8214 \][/tex]

Thus, the final cost for purchasing in the physical store is:
[tex]\[ \$77.8214 \][/tex]

### Online Store Purchase

1. Calculating Total Cost Before Discounts and Shipping:
- Headphones: [tex]\(1 \times \$13.50 = \$13.50\)[/tex]
- DVDs: [tex]\(4 \times \$14.99 = \$59.96\)[/tex]
- CDs: [tex]\(2 \times \$10.99 = \$21.98\)[/tex]

Summing these amounts gives us the total cost:
[tex]\[ \$13.50 + \$59.96 + \$21.98 = \$95.44 \][/tex]

2. Applying [tex]$20.00 Discount: - Discount amount: \(\$[/tex]20.00\)

Subtract the discount from the total cost:
[tex]\[ \$95.44 - \$20.00 = \$75.44 \][/tex]

3. Considering Shipping Costs:
- Since the total after discount (\[tex]$75.44) is above the free shipping threshold of \$[/tex]75.00, the shipping cost is \[tex]$0.00. Hence, the final cost for purchasing online is: \[ \$[/tex]75.44
\]

### Decision on Purchasing Method

Comparing the final costs:
- Physical store: [tex]\(\$77.8214\)[/tex]
- Online store: [tex]\(\$75.44\)[/tex]

The most cost-effective option is to purchase the items online, with a total cost of [tex]\(\$75.44\)[/tex]. This option saves you the most money.

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