Question

akio goes shopping for a sports jersey at the local teams fan store and finds one that retails for $100. the local sales tax rate is 5.75%. currently the store is advertising a 35% discount on all jerseys.
determine the final cost.
base cost + factor 1 + factor 2 = total cost
$ 100.00 * * = $
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 35% 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: Calculate discount factor

A 35% discount means we pay \(100\% - 35\% = 65\%\) of the base cost. Convert 65% to a decimal: \(65\%=\frac{65}{100} = 0.65\). So Factor 1 (discount factor) is \(0.65\).

Step2: Calculate tax factor

A 5.75% tax means we pay \(100\%+ 5.75\%=105.75\%\) of the discounted cost. Convert 105.75% to a decimal: \(105.75\%=\frac{105.75}{100}=1.0575\). So Factor 2 (tax factor) is \(1.0575\).

Step3: Calculate final cost

First, apply the discount: \(100\times0.65 = 65\). Then apply the tax: \(65\times1.0575=68.7375\approx68.74\).

Answer:

The final cost is \(\$68.74\) (if we consider two - decimal places for currency). If we follow the exact calculation from the factors: \(100\times0.65\times1.0575 = 68.7375\), so the final cost is \(\$68.74\) (rounded to the nearest cent) or \(\$68.7375\) (exact value).