Question

harvey is shopping for a new desk lamp and finds that the home goods store is selling one for $11.75. the local sales tax rate is 6.25%. he has a coupon for thirty percent off the retail price.
determine the final cost.
base cost factor 1 factor 2 = total cost
$ * * = $
i want to do the optional tasks.
adding a 6.25% tax to the base cost of an item is the same as multiplying the base cost of the item by what decimal factor?
subtracting a 30% discount from the base cost of an item is the same as multiplying the base cost of the item by what decimal factor?

Explanation:

Step1: Understand the tax addition

When adding a tax of 6.25% to the base cost, we need to find the factor that represents the base cost plus the tax. The tax is 6.25% of the base cost, so the total cost is base cost + 6.25% of base cost.
Mathematically, this is \( \text{Base Cost} + 0.0625 \times \text{Base Cost} \).

Step2: Factor out the base cost

Factor out the base cost from the expression: \( \text{Base Cost} \times (1 + 0.0625) \).
Calculate \( 1 + 0.0625 = 1.0625 \).
So adding a 6.25% tax is the same as multiplying the base cost by 1.0625.

For the discount part:

Step1: Understand the discount subtraction

When subtracting a 30% discount from the base cost, we need to find the factor that represents the base cost minus the discount. The discount is 30% of the base cost, so the total cost after discount is base cost - 30% of base cost.
Mathematically, this is \( \text{Base Cost} - 0.30 \times \text{Base Cost} \).

Step2: Factor out the base cost

Factor out the base cost from the expression: \( \text{Base Cost} \times (1 - 0.30) \).
Calculate \( 1 - 0.30 = 0.70 \).
So subtracting a 30% discount is the same as multiplying the base cost by 0.70.

Now, for the final cost of the desk lamp:

Step1: Find the price after discount

The base price is $11.75. First, apply the 30% discount. Multiply the base price by 0.70 (from the discount factor).
\( 11.75 \times 0.70 = 8.225 \).

Step2: Apply the sales tax

Now, apply the 6.25% sales tax to the discounted price. Multiply the discounted price by 1.0625 (from the tax factor).
\( 8.225 \times 1.0625 = 8.7390625 \approx 8.74 \) (rounded to the nearest cent).

Answer:

• Tax factor: 1.0625
• Discount factor: 0.70
• Final cost: $8.74