Let's analyze the given problem step-by-step to determine which expressions correctly show the total taxes you would expect to pay in Philadelphia, PA, for a bottle of sports drink priced at [tex]$2.
### Problem Breakdown:
- Shelf price of the bottle: $[/tex]2
- State sales tax in Pennsylvania: [tex]\(6\% = 0.06\)[/tex]
- Local sales tax in Philadelphia: [tex]\(2\% = 0.02\)[/tex]
- Both taxes are applied to the original price.
### Calculation of Taxes:
1. Total tax rate:
The total tax rate is the sum of the state and local sales tax rates.
[tex]\[
\text{Total tax rate} = 0.06 + 0.02 = 0.08
\][/tex]
2. Total tax amount:
The total tax amount is the product of the shelf price and the total tax rate.
[tex]\[
\text{Total tax} = 2 \times 0.08
\][/tex]
### Step-by-Step Analysis of Each Expression:
1. Expression: [tex]\(2(0.06 + 0.02)\)[/tex]
- This expression calculates the total tax rate and then multiplies it by the price:
[tex]\[
2 \times (0.06 + 0.02) = 2 \times 0.08 = 0.16
\][/tex]
- This correctly represents the total tax amount.
2. Expression: [tex]\(2(0.06)(2)(0.02)\)[/tex]
- This expression multiplies the price by each of the tax rates separately, and then multiplies all the terms together:
[tex]\[
2 \times 0.06 \times 2 \times 0.02 = 2 \times 2 \times 0.06 \times 0.02 = 4 \times 0.0012 = 0.0048
\][/tex]
- This does not correctly represent the calculation of the taxes.
3. Expression: [tex]\(2 + 0.06 + 0.02\)[/tex]
- This expression simply adds the price of the item to the tax rates individually:
[tex]\[
2 + 0.06 + 0.02 = 2.08
\][/tex]
- This expression does not represent the calculation of the total tax.
4. Expression: [tex]\(2(0.06) + 2(0.02)\)[/tex]
- This expression calculates each part of the tax rate separately and then adds them together:
[tex]\[
2 \times 0.06 + 2 \times 0.02 = 0.12 + 0.04 = 0.16
\][/tex]
- This correctly represents the total tax amount.
### Conclusion:
The correct expressions to show the total taxes you would expect to pay in Philadelphia, PA, are:
[tex]\[
2(0.06 + 0.02) \quad \text{and} \quad 2(0.06) + 2(0.02)
\][/tex]
Both expressions yield the result [tex]$0.16, which represents the total tax added to the shelf price of $[/tex]2.
