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.
