Let's solve the problem step-by-step.
1. Identify the relevant information:
- Cost of the furniture set in both states: \[tex]$1500
- Tax rates:
- Alabama:
- State tax: 4.225%
- County tax: 1.375%
- City tax: 3.0%
- Florida:
- State tax: 6.5%
- County tax: 1.0%
- City tax: 1.625%
2. Calculate the total tax rates in both states:
- Alabama:
\[
\text{Total tax rate in Alabama} = 4.225\% + 1.375\% + 3.0\% = 8.6\%
\]
- Florida:
\[
\text{Total tax rate in Florida} = 6.5\% + 1.0\% + 1.625\% = 9.125\%
\]
3. Convert the percentage rates to decimals for calculation:
- Alabama:
\[
8.6\% = 0.086
\]
- Florida:
\[
9.125\% = 0.09125
\]
4. Calculate the sales tax amount for the furniture set in both states:
- Alabama:
\[
\text{Sales tax amount in Alabama} = 1500 \times 0.086 = 129 \text{ dollars}
\]
- Florida:
\[
\text{Sales tax amount in Florida} = 1500 \times 0.09125 = 136.875 \text{ dollars}
\]
5. Determine the difference in sales tax amounts between the two states:
\[
\text{Difference} = |129 - 136.875| = 7.875 \text{ dollars}
\]
6. Analyze the statements given in the question:
- A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about \$[/tex]8.
- B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about \[tex]$10.
- C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by \$[/tex]10.
- D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations.
Considering the calculations:
- The difference in sales tax is approximately \[tex]$7.875.
- Since the difference is below \$[/tex]8, we can conclude that the sales taxes in both states are very close.
The correct statement is:
D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations.
