Answer :
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.
### 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.
