In addition to the regular trade discount of 25% and a volume purchase discount of 8.33333333% from the manufacturer, Appliance Warehouse is offered a further 5% discount for orders places in January.
a. What is the list price on an electric range whose net price works out to be $470.25
b. What single trade discount rate is equivalent to the three trade discounts?
c. After the regular and volume discounts are both taken, what dollar amount of savings does the extra discount for January orders represent on a $1000 list price item?
a. To find the list price on an electric range, when the net price is given, we need to calculate the original price before any discounts.
Let's start by subtracting the extra discount offered in January. The net price is $470.25, and the extra discount in January is 5%.
$470.25 - (5/100) * $470.25
Simplifying the above expression, we get:
$470.25 - 0.05 * $470.25
Simplifying further, we find:
$470.25 - $23.513
Therefore, the price after the January discount is $446.7375.
Next, we need to consider the regular trade discount of 25% from the manufacturer. To find the price before this discount, we need to divide the current price by 1 minus the discount rate.
$446.7375 ÷ (1 - 25/100)
Simplifying the above expression, we get:
$446.7375 ÷ 0.75
This results in a price of $595.65.
Finally, we account for the volume purchase discount of 8.33333333%. To find the price before this discount, we divide the current price by 1 minus the discount rate.
$595.65 ÷ (1 - 8.33333333/100)
Simplifying the above expression, we get:
$595.65 ÷ 0.916666667
This results in a price of $650.
Therefore, the list price on the electric range is $650.
b. To find the single trade discount rate that is equivalent to the three trade discounts, we need to calculate the overall discount percentage.
The first discount is 25%, the second discount is 8.33333333%, and the third discount is 5%. To find the overall discount percentage, we subtract each discount from 100% and multiply the resulting values together.
Overall Discount Percentage = (100% - 25%) * (100% - 8.33333333%) * (100% - 5%)
Simplifying the above expression, we get:
Overall Discount Percentage = 75% * 91.66666667% * 95%
Calculating this expression, we find the overall discount percentage is 64.0625%.
Therefore, the single trade discount rate that is equivalent to the three trade discounts is approximately 64.0625%.
c. To find the dollar amount of savings represented by the extra discount for January orders on a $1000 list price item, we need to calculate the amount saved through the January discount.
The list price of the item is given as $1000, and the extra discount for January orders is 5%.
Savings through January discount = (5/100) * $1000
Simplifying the above expression, we find:
Savings through January discount = $50
Therefore, the extra discount for January orders represents a savings of $50 on a $1000 list price item.