To determine which bed is the better deal, we need to calculate the final cost of each bed after applying the discount or rebate, as well as the sales tax. Let's go through the steps one by one.
### Bed 1
1. Original Cost: [tex]$480
2. Discount: 15%
First, we calculate the discount amount:
\[ \text{Discount Amount} = \$[/tex]480 \times 0.15 = \[tex]$72 \]
Subtract the discount from the original cost to get the discounted price:
\[ \text{Discounted Price} = \$[/tex]480 - \[tex]$72 = \$[/tex]408 \]
Next, we calculate the sales tax on the discounted price (5%):
[tex]\[ \text{Sales Tax for Bed 1} = \$408 \times 0.05 = \$20.40 \][/tex]
Add the sales tax to the discounted price to get the final price:
[tex]\[ \text{Final Price for Bed 1} = \$408 + \$20.40 = \$428.40 \][/tex]
### Bed 2
1. Original Cost: [tex]$454
2. Rebate: $[/tex]30
First, subtract the rebate from the original cost to get the rebated price:
[tex]\[ \text{Rebated Price} = \$454 - \$30 = \$424 \][/tex]
Next, we calculate the sales tax on the rebated price (5%):
[tex]\[ \text{Sales Tax for Bed 2} = \$424 \times 0.05 = \$21.20 \][/tex]
Add the sales tax to the rebated price to get the final price:
[tex]\[ \text{Final Price for Bed 2} = \$424 + \$21.20 = \$445.20 \][/tex]
### Comparing the Final Prices
- Final Price for Bed 1: [tex]$428.40
- Final Price for Bed 2: $[/tex]445.20
The better deal is the one with the lower final price.
Therefore, Bed 1 is the better deal with a final price of $428.40.
