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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.
### 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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