Solving a 20% Profit Problem: Bernie's Bargain Basement

[zak100]

Homework Statement

At bernie's Bargain basement everything is sold for 20% less than the 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

To increase a number by K% multiply it by (1+k%)

The Attempt at a Solution

For profit he has to increase the price by 20%.
Two ways: 20/100 * (80) =16 and then 80 + 16 = 96
OR 80(1+20/100) = 80 * 1.2 = 96

Now this is the profit price but he is giving a discount of 20% also by retaining the 20 % profit. This means we have to increase the profit price by 20%
96(1.2) =115.2 but this is not correct. Somebody please guide me.

Zulfi.

 

[Bystander]

What are the two basis prices? Ninety-six and something times ninety-six.

This means we have to increase the profit price by 20%

Are you certain?

 

[SammyS]

Homework Statement

At bernie's Bargain basement everything is sold for 20% less than the 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

To increase a number by K% multiply it by (1+k%)

The Attempt at a Solution

For profit he has to increase the price by 20%.
Two ways: 20/100 * (80) =16 and then 80 + 16 = 96
OR 80(1+20/100) = 80 * 1.2 = 96

Now this is the profit price but he is giving a discount of 20% also by retaining the 20 % profit. This means we have to increase the profit price by 20%
96(1.2) =115.2 but this is not correct. Somebody please guide me.

Zulfi.

I agree that $115.20 is not the correct answer.

How can you tell that this is not the correct answer ?

 

[zak100]

Hi,
I have found the profit price which is 96. Now I have to find the marked price. Then I would deduct 20% from it. Am I right?

Zulfi.

 

[SammyS]

W

Hi,
I have found the profit price which is 96. Now I have to find the marked price. Then I would deduct 20% from it. Am I right?

Zulfi.

What I asked was regarding how to check your answer.

Take $115.20 as the marked price.

Then Bernie knocks 20% off of that, meaning he only charges 80% of that which is $92.16 .

Therefore, Bernie's profit would be $12.16, but that is only 15.2% of $80 , so $115.20 is incorrect.I suggest:
Let x represent the marked price. Then go through the above process using x rather than $115.20. Equate the result to 0.20, i.e. 20%. Turn that into an equation. Solve for x.

 

[Chestermiller]

I agree with SammyS. If x is the marked price, what is the price that the item is sold at (in terms of x)?

 

[zak100]

Hi,
it would be x(1-20/100) = x(0.8). This is because we have to deduct a discount of 20% from the marked price which we supposed to be x.
<
Equate the result to 0.20, i.e. 20%. >

Sorry.
What the book did is that they equated it to : 96 which I can't understand. That is they did:
96 = x (.8)
So please guide me why 20 % discount from marked price is equal to profit price??
Zulfi.

 

[SammyS]

Hi,
it would be x(1-20/100) = x(0.8). This is because we have to deduct a discount of 20% from the marked price which we supposed to be x.
<
Equate the result to 0.20, i.e. 20%. >

Sorry.
What the book did is that they equated it to : 96 which I can't understand. That is they did:
96 = x (.8)
So please guide me why 20 % discount from marked price is equal to profit price??
Zulfi.

You got the $96 previously. Right?

Bernie wants his profit to equal 20% of his cost. That's 20% of $80 which is $16, so he must charge $96.

 

[Chestermiller]

Hi,
it would be x(1-20/100) = x(0.8). This is because we have to deduct a discount of 20% from the marked price which we supposed to be x.
<
Equate the result to 0.20, i.e. 20%. >

Sorry.
What the book did is that they equated it to : 96 which I can't understand. That is they did:
96 = x (.8)
So please guide me why 20 % discount from marked price is equal to profit price??
Zulfi.

The list price is $120. The discount price is $96. This gives the owner a 20% profit over the cost of $80.

If you want to offer your customer a 20% discount on the list price and also want to make 20% above your cost, your list price must be 50% above your cost (not matter what your cost is).

 

[zak100]

Okay.
96 = x(.8)
LHS is equal to RHS

96 is the disount price.
x represents the 'marked price.
0.8 represents discount of 20%. i.e the term (1- 20/100). Because of the discount we are subtracting.

Thanks.

Zulfi.