Calculate the net price factor and net price (in dollars). For convenience, round the net price factor to five decimal places and the net price to the nearest cent, when necessary.

[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline
\text{List Price} & \text{Trade Discount Rate} & \text{Net Price Factor} & & \text{Net Price} & \\
\hline
\$455.60 & 22\% / 15\% / 5\% & 78\% & x & \$355.37 & x \\
\hline
\end{array}
\][/tex]



Answer :

To find the net price factor and the net price, let's follow a step-by-step approach.

### Step 1: Calculate the Trade Discount Factor

Given trade discount rates of 22%, 15%, and 5%, we need to apply each discount sequentially to the list price.

Conversion of percentage to decimal:
- 22% = 0.22
- 15% = 0.15
- 5% = 0.05

The formula to calculate the trade discount factor is:
[tex]\[ \text{Trade Discount Factor} = (1 - \text{Rate1}) \times (1 - \text{Rate2}) \times (1 - \text{Rate3}) \][/tex]

Plugging in the rates:
[tex]\[ \text{Trade Discount Factor} = (1 - 0.22) \times (1 - 0.15) \times (1 - 0.05) \][/tex]
[tex]\[ = 0.78 \times 0.85 \times 0.95 \][/tex]

Computing this gives:
[tex]\[ \text{Trade Discount Factor} \approx 0.6291 \][/tex]

### Step 2: Calculate the Net Price Factor

The Net Price is expressed as a percentage of the trade-discounted price. Given that the net price percentage is 78% (or 0.78 as a decimal):

[tex]\[ \text{Net Price Factor} = \text{Trade Discount Factor} \times \text{Net Price Percentage} \][/tex]
[tex]\[ \text{Net Price Factor} = 0.6291 \times 0.78 \][/tex]
[tex]\[ \text{Net Price Factor} \approx 0.49128 \][/tex]

### Step 3: Calculate the Net Price

Given the list price of \[tex]$455.60, the net price is calculated by multiplying this by the net price factor: \[ \text{Net Price} = \text{List Price} \times \text{Net Price Factor} \] \[ \text{Net Price} = 455.60 \times 0.49128 \] \[ \text{Net Price} \approx 223.83 \] ### Step 4: Rounding the Results - The net price factor rounded to five decimal places: \(0.49128\) - The net price rounded to the nearest cent: \(\$[/tex]223.83\)

### Conclusion
- Net Price Factor (rounded to five decimal places): 0.49128
- Net Price (rounded to the nearest cent): \[tex]$223.83 So, the net price factor is 0.49128 and the net price is \$[/tex]223.83.