A second hand furniture store buys sofas with a list price of $9,500. If the wholesaler offers trade discounts of 10/20/30, find the single equivalent discount.
single equivalent discount
= 1 - .9(.8)(.7) = .496 = 49.6%
49.6% off 9500 = 4712
final price = 9500-4712 = 4788
or , the long way
10% of 9500 = 950
after 1st discount: 9500-950 = 8550
20% discount on 8550 = 1710
after 2nd discount:8550-1710 = 6840
30% of 6840 = 2052
after 3rd discount: 6840-2052 = 4788
Well, it seems like the wholesaler really wants to make it confusing for you. They couldn't settle on just one discount, so they decided to offer a series of discounts, like a menu of discounts. It's like going to a buffet, but instead of food, it's discounts!
So, let me break it down for you. The wholesaler is offering three different trade discounts: 10%, 20%, and 30%. Now, to find the single equivalent discount, we need to calculate the total discount you'll be getting off the list price of $9,500.
First, let's start with the 10% discount. If we take 10% off $9,500, we'll get $950. That's a nice little chunk of change.
Next up, we have the 20% discount. If we take 20% off the original price, we'll get $1,900. That's a bit more substantial.
Lastly, we have the 30% discount. Taking 30% off $9,500 gives us a whopping $2,850. That's getting closer to some serious savings.
Now, to find the single equivalent discount, we add up all these individual discounts. So, $950 + $1,900 + $2,850 = $5,700.
Voila! The single equivalent discount offered by the wholesaler is $5,700. That's quite a generous discount, if you ask me. Maybe they're trying to sell those sofas real bad. Happy sofa shopping!
To find the single equivalent discount for trade discounts of 10/20/30, we need to calculate the total discount percentage.
Step 1: Calculate the net amount after the first discount:
List price = $9,500
First discount = 10%
Net amount after first discount = List price - (Discount percentage x List price)
Net amount after first discount = $9,500 - (10/100 x $9,500)
Net amount after first discount = $9,500 - $950
Net amount after first discount = $8,550
Step 2: Calculate the net amount after the second discount:
Second discount = 20%
Net amount after second discount = Net amount after first discount - (Discount percentage x Net amount after first discount)
Net amount after second discount = $8,550 - (20/100 x $8,550)
Net amount after second discount = $8,550 - $1,710
Net amount after second discount = $6,840
Step 3: Calculate the net amount after the third discount:
Third discount = 30%
Net amount after third discount = Net amount after second discount - (Discount percentage x Net amount after second discount)
Net amount after third discount = $6,840 - (30/100 x $6,840)
Net amount after third discount = $6,840 - $2,052
Net amount after third discount = $4,788
Step 4: Calculate the single equivalent discount:
Single equivalent discount = (List price - Net amount after third discount) / List price * 100%
Single equivalent discount = ($9,500 - $4,788) / $9,500 * 100%
Single equivalent discount = $4,712 / $9,500 * 100%
Single equivalent discount ≈ 49.6%
Therefore, the single equivalent discount for trade discounts of 10/20/30 is approximately 49.6%.
To find the single equivalent discount, we need to take into account the series of trade discounts offered.
Let's break down the trade discounts:
10/20/30 implies:
- A 10% discount is applied first
- Then a 20% discount is applied to the remaining amount after the initial discount
- Finally, a 30% discount is applied to the remaining amount after the second discount
To calculate the single equivalent discount, we will find the equivalent amount of the final selling price compared to the list price.
Step 1: Apply the first discount of 10%
The amount after the first discount is:
$9,500 - (10/100) * $9,500 = $9,500 - $950 = $8,550
Step 2: Apply the second discount of 20%
The amount after the second discount is:
$8,550 - (20/100) * $8,550 = $8,550 - $1,710 = $6,840
Step 3: Apply the third discount of 30%
The final selling price after all the trade discounts is:
$6,840 - (30/100) * $6,840 = $6,840 - $2,052 = $4,788
Now, let's calculate the single equivalent discount:
Discount = List Price - Final Selling Price
Discount = $9,500 - $4,788 = $4,712
The single equivalent discount is $4,712.