You are making several purchases from B-Better Electronics. You can buy online or in-store. You have:

- A 20% off coupon for in-store purchases.
- A [tex]$20.00 off coupon for online purchases.
- A sales tax of 7.5% for in-store purchases.
- A shipping fee of $[/tex]8.99 for online purchases, which is waived for purchases over [tex]$75.00.

Determine which option saves you the most money. Include:

1. Steps for your computations.
2. Your choice of purchase method.
3. The total cost of your purchases.

\ \textless \ strong\ \textgreater \ Prices at B-Better Electronics Store:\ \textless \ /strong\ \textgreater \
| Item | Quantity | Price per Item |
|------------|----------|----------------|
| Headphones | 1 pair | $[/tex]14.99 |
| DVDs | 4 | [tex]$13.95 |
| CDs | 2 | $[/tex]9.85 |

Prices at Online Store:
| Item | Quantity | Price per Item |
|------------|----------|----------------|
| Headphones | 1 pair | [tex]$13.50 |
| DVDs | 4 | $[/tex]14.99 |
| CDs | 2 | $10.99 |

To determine whether it is cheaper to purchase the items in-store or online, we need to calculate the total costs for each option while considering discounts, taxes, and shipping fees. Let's go through the calculations step by step.

### Step 1: Calculate the Total Cost for In-Store Purchase

#### Item Costs Before Discounts and Taxes:
- Headphones: \[tex]$14.99 $\times 1 = \$[/tex]14.99$
- DVDs: \[tex]$13.95 $\times 4 = \$[/tex]55.80$
- CDs: \[tex]$9.85 $\times 2 = \$[/tex]19.70$

Adding these together, the total before any discounts or taxes is:
[tex]\[ \$14.99 + \$55.80 + \$19.70 = \$90.49 \][/tex]

#### Applying the 20% Discount:
The store offers a 20% discount. To calculate the 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]

#### Applying the 7.5% Sales Tax:
The sales tax only applies after the discount. Calculate the sales tax amount:
[tex]\[ 0.075 \times 72.392 = 5.4294 \][/tex]

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

So, the final cost for in-store purchase is:
[tex]\[ \$77.8214 \][/tex]

### Step 2: Calculate the Total Cost for Online Purchase

#### Item Costs:
- Headphones: \[tex]$13.50 $\times 1 = \$[/tex]13.50$
- DVDs: \[tex]$14.99 $\times 4 = \$[/tex]59.96$
- CDs: \[tex]$10.99 $\times 2 = \$[/tex]21.98$

Adding these together, the total is:
[tex]\[ \$13.50 + \$59.96 + \$21.98 = \$95.44 \][/tex]

#### Applying the \[tex]$20.00 Coupon: Subtract the coupon: \[ \$[/tex]95.44 - \[tex]$20.00 = \$[/tex]75.44
\]

#### Considering Shipping Cost:
The online store offers free shipping for orders over \[tex]$75.00. Since our total after the coupon is \$[/tex]75.44, shipping is free:
[tex]\[ Shipping = \$0.00 \][/tex]

So, the final cost for online purchase is:
[tex]\[ \$75.44 \][/tex]

### Step 3: Compare the Costs to Determine the Cheapest Option

- Total cost in-store: \[tex]$77.8214 - Total cost online: \$[/tex]75.44

Comparing the two, purchasing the items online saves money.

### Conclusion

The cheaper option is to purchase the items online. The total cost for purchasing online is:
[tex]\[ \$75.44 \][/tex]