Of course! Let's break down the solution step-by-step:
### Part (a) - Calculate the price after a 25% discount:
1. Original Price of the Shirt:
The initial price of the shirt is [tex]$75.
2. Discount Percentage:
The discount offered is 25%.
3. Calculate the Discount Amount:
To find the discount amount, multiply the original price by the discount percentage (expressed as a decimal).
\[
\text{Discount Amount} = 75 \times \frac{25}{100} = 18.75
\]
4. Calculate the Discounted Price:
Subtract the discount amount from the original price.
\[
\text{Discounted Price} = 75 - 18.75 = 56.25
\]
So, the price of the shirt after a 25% discount is $[/tex]56.25.
### Part (b) - Calculate the final price with a 6% tax:
1. Discounted Price of the Shirt:
We found that the discounted price is [tex]$56.25.
2. Tax Percentage:
The state tax rate is 6%.
3. Calculate the Tax Amount:
To find the tax amount, multiply the discounted price by the tax percentage (expressed as a decimal).
\[
\text{Tax Amount} = 56.25 \times \frac{6}{100} = 3.375
\]
4. Calculate the Final Price:
Add the tax amount to the discounted price.
\[
\text{Final Price} = 56.25 + 3.375 = 59.625
\]
Therefore, the final price of the shirt, including a 6% state tax, is $[/tex]59.625.
