Selling price for an item with a markup and discount

[zak100]

Homework Statement

At Bernie’s Bargain everything is sold for 20% less than the marked price marked. If Bernie buys radios for 80$, what price should he mark them if he wants to make a 20% profit on his cost?

Homework Equations

I don’t know the equation for selling price. From Internet I got this:

SP – cost = gross margin
But this is not working:
SP -80 = 40%
SP – 0.4 = 80
0.6SP = 80
SP = 133.33
Which is wrong

The Attempt at a Solution

Calculating the profit on 80$.
20/100 * 80 = 16
There after adding profit to the cost we get 96$. Now I don’t know how to find the selling price in which we would adding the 20% discount also.
Some body please guide me.

Zulfi.

 

[mjc123]

There after adding profit to the cost we get 96$. Now I don’t know how to find the selling price

That is the selling price to get 20% profit on cost. The question asks, what price should he mark them if he intends to sell them at $96, and he sells everything at 20% less than the marked price?

 

[zak100]

Hi,
Is there any formula for this, specific to selling price or something related to percentage which the book has provided?

Zulfi.

 

[Ray Vickson]

Hi,
Is there any formula for this, specific to selling price or something related to percentage which the book has provided?

Zulfi.

So, you do not know the marked price? Just call it $x$. Now set up an equation for $x$ and solve it.

 

[SammyS]

Homework Statement

At Bernie’s Bargain everything is sold for 20% less than the marked price marked. If Bernie buys radios for 80$, what price should he mark them if he wants to make a 20% profit on his cost?

Homework Equations

I don’t know the equation for selling price. From Internet I got this:

SP – cost = gross margin
But this is not working:
SP -80 = 40%
SP – 0.4 = 80
0.6SP = 80
SP = 133.33
Which is wrong

The Attempt at a Solution

Calculating the profit on 80$.
20/100 * 80 = 16
There after adding profit to the cost we get 96$. Now I don’t know how to find the selling price in which we would adding the 20% discount also.
Some body please guide me.

Zulfi.

Don't be concerned about finding some formula. Use reasoning.

Bernie wants to make a profit of 20% on his cost.

What is 20% of his cost ?

The answer to this is the profit he needs to make on each radio.​

Take it from there, a step at a time.

 

[zak100]

Hi,
I am able to find the cost + profit which is 96.

The question asks, what price should he mark them if he intends to sell them at $96

I think the question means:
The question asks, what price should he mark them if he intends to get $96. Thus the price he would mark would be greater than 96$. The mark price or selling price not known. If its greater than 96$ then we should use following:
If a number is the result of increasing another number by K% , to find original number divide by (1 + k%).
i.e x (Selling price) = 96/(1 + 0.2)
but answer is not correct. Some body please guide me.

Zulfi.

 

[SammyS]

Hi,
I am able to find the cost + profit which is 96.

I think the question means:
The question asks, what price should he mark them if he intends to get $96. Thus the price he would mark would be greater than 96$. The mark price or selling price not known. If its greater than 96$ then we should use following:
If a number is the result of increasing another number by K% , to find original number divide by (1 + k%).
i.e x (Selling price) = 96/(1 + 0.2)
but answer is not correct. Some body please guide me.

Zulfi.

You have that backwards.

Bernie marks a price so that when he takes 20% off that price, the amount he actually charges leaves him with the original cost plus the desired profit.

 

[rcgldr]

To make a 20% of the cost profit, the selling price needs to be $80 * (1 + 0.20) = $96. To get that selling price of $96 after a 20% discount, start with the equation sticker_price * (1 - 0.20) = selling_price = $96.

 

[zak100]

Hi,
Thanks. You have lighted the think which i was not able to understand. According to book, to decrease a number by K% multiply it by 1-K%. But sticker_price should be greater than 96$, so why are we decreasing. Thanks for your efforts.Zulfi.

 

[LCKurtz]

To make a 20% of the cost profit, the selling price needs to be $80 * 1.2 = $96. To get that selling price of $96 after a 20% discount, start with the equation sticker_price * (1 - 0.20) = selling_price = $96.

Hi,
Thanks. You have lighted the think which i was not able to understand. According to book, to decrease a number by K% multiply it by 1-K%. But sticker_price should be greater than 96$, so why are we decreasing. Thanks for your efforts.

Zulfi.

In the equation rcgldr gave you: sticker_price * (1 - 0.20) = $96, the sticker_price is unknown. Solve the equation for it. You are decreasing it because your customer is going to want a discount from the sticker price and you still want to get $96. Solving for the sticker price will tell you what you need to put on the price tag so that after the discount you still get $96.

 

[zak100]

Hi,
Thanks. I think, i must accept this as an answer. Thanks for your energies.

Zulfi.

 

[SammyS]

Hi,
Thanks. I think, i must accept this as an answer. Thanks for your energies.

Zulfi.

What is your final solution to this problem? Notice that once you get an answer, you can easily check it.

We would like to see that worked out.

 

[zak100]

Hi,
Thanks for you concerns. Good. Actually I knew the answer. But I was not able to understand why were we using the formula:
If a number is the result of decreasing another number by K% , to find original number divide by (1 - k%). i.e.:
x = 96/(1-20/100)
Or what rcgldr provided:

sticker_price * (1 - 0.20) = $96

Reference https://www.physicsforums.com/threads/selling-price-for-an-item-with-a-markup-and-discount.918917/
Replacing sticker_price by x, we have:

X * (1-0.2) = 96

X * 0.8 = 96

X = 96/0.8 *10/ 10

= 960/8 = 120

I once tried to verify the result correctly but now I forget.

Zulfi.

 

[SammyS]

Hi,
...

Replacing sticker_price by x, we have:

X * (1-0.2) = 96

X * 0.8 = 96

X = 96/0.8 *10/ 10

= 960/8 = 120

I once tried to verify the result correctly but now I forget.

Zulfi.

To verify the answer:

Sticker price: $120.

Bernie charges 80% of that, i.e. 20% off of marked price:

That's 80% of $120 is $96.​

That's a profit of $16.

$16/$80 = 0.20 → 20%

 

[zak100]

Hi,
Thanks for this additional work.

God bless you.

Zulfi.