At the hardware store, you purchase a box of nails originally worth [tex]$\$[/tex]12.95[tex]$. You have a coupon for $[/tex]20\%[tex]$ off the nails. Sales tax is $[/tex]6\%[tex]$. What is the total cost for the nails?

Discounted Subtotal $[/tex]=[tex]$ Subtotal $[/tex]\times (1-\text{off percentage})[tex]$

Total $[/tex]=[tex]$ Discounted Subtotal $[/tex]\times (1+\text{sales tax percentage})[tex]$

A. $[/tex]\[tex]$10.98$[/tex]
B. [tex]$\quad \$[/tex]11.96[tex]$
C. $[/tex]\[tex]$12.68$[/tex]



Answer :

Certainly! Let's follow the steps to determine the total cost for the nails after applying both the discount and the sales tax.

1. Original Price:
The original price of the box of nails is \[tex]$12.95. 2. Applying the Discount: You have a coupon that gives you a 20% discount. First, we need to calculate the amount of discount: \[ \text{Discount amount} = \text{Original Price} \times \text{Discount Percent} \] \[ \text{Discount amount} = 12.95 \times 0.20 = 2.59 \] Subtract the discount amount from the original price to get the discounted subtotal: \[ \text{Discounted Subtotal} = \text{Original Price} - \text{Discount amount} \] \[ \text{Discounted Subtotal} = 12.95 - 2.59 = 10.36 \] 3. Calculating the Sales Tax: The sales tax is 6%. We need to calculate the sales tax on the discounted subtotal: \[ \text{Sales Tax Amount} = \text{Discounted Subtotal} \times \text{Sales Tax Percent} \] \[ \text{Sales Tax Amount} = 10.36 \times 0.06 = 0.6216 \] 4. Total Cost: Add the sales tax amount to the discounted subtotal to get the total cost: \[ \text{Total Cost} = \text{Discounted Subtotal} + \text{Sales Tax Amount} \] \[ \text{Total Cost} = 10.36 + 0.6216 = 10.9816 \] When rounded to two decimal places (since we're dealing with currency), the total cost is approximately \$[/tex]10.98.

Thus, the correct answer is:

A. \$10.98