Question

kordell needs a new pillar candle. the craft store has one in stock that kordell likes for $6.55. the local sales tax rate is 5.75%. he has a coupon for five percent off the retail price.
determine the final cost.
base cost factor 1 factor 2 = total cost
$ 6.55 * 0.95 * = $
i want to do the optional tasks.
adding a 5.75% 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 5 % discount from the base cost of an item is the same as multiplying the base cost of the item by what decimal factor?
when calculating the total cost of a discounted item to which sales tax applies, one must multiply the base cost

Explanation:

Step1: Identify the factors

The base cost is $6.55, Factor 1 (discount factor) is 0.95 (since 5% off means we pay 95% or 0.95 of the base cost), and Factor 2 is the tax factor. To find the tax factor, we add the tax rate to 1. The tax rate is 5.75%, so as a decimal, that's 0.0575. So the tax factor is \(1 + 0.0575 = 1.0575\).

Step2: Calculate the total cost

Now we multiply the base cost by Factor 1 and then by Factor 2. So first, \(6.55\times0.95\) gives the discounted price, then multiply by 1.0575 for tax. Let's compute \(6.55\times0.95 = 6.2225\). Then, \(6.2225\times1.0575\approx6.2225\times1.0575\). Let's calculate that: \(6.2225\times1 = 6.2225\), \(6.2225\times0.05 = 0.311125\), \(6.2225\times0.0075 = 0.04666875\). Adding those together: \(6.2225 + 0.311125 + 0.04666875 = 6.58029375\). So approximately $6.58.

Answer:

The total cost is approximately \(\$6.58\) (or more precisely, using the formula \(6.55\times0.95\times1.0575 = 6.55\times(0.95\times1.0575)\). Calculating \(0.95\times1.0575 = 1.004625\), then \(6.55\times1.004625 = 6.55 + 6.55\times0.004625 = 6.55 + 0.03029375 = 6.58029375\), so \(\$6.58\) when rounded to the nearest cent).