Marked Price for 20% Discount Sofa with 25% Profit

  • MHB
  • Thread starter paulmdrdo1
  • Start date
In summary: We're also told:D=0.8Mso:1.25C=0.8MC=0.64MWe're also given:C=$1200.64M=120M=120/0.64=187.5So the marked price should be $187.50.In summary, the problem asks for the marked price of a sofa that costs $120, given a discount of 20% on the marked price and a profit of 25% on the selling price. Using the equations C + P = S and D = 0.8M, where C = cost, P = profit, S = sale price, and D = discounted price,
  • #1
paulmdrdo1
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At what price should a merchant mark a sofa that costs \$120 in order that it may be offered at a discount of 20% on the marked price and still make a profit of 25% on the selling price?

I'm confused about this problem. can you please help me solve this one?

this where I can get to,

let $x=$ marked price; $x-0.2x=$ sale price. then, $0.8x=$ sale price.

now I don't know how to set up the proper equation. please help.
 
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  • #2
Re: profit problems

Should not the marked price $x$ be such that:

$0.75(0.8x) = 120$?
 
  • #3
Re: profit problems

$x=200$ but how you did get that 0.75 multiplied by the sale price? I don't understand.
 
  • #4
I would let $C$ be the cost, $D$ be the discounted price, and $M$ be the marked price. We then require:

\(\displaystyle D=0.8M\)

\(\displaystyle D=1.25C\)

Hence:

\(\displaystyle 0.8M=1.25C\)

So what do you find the marked price should be?
 
  • #5
Re: profit problems

paulmdrdo said:
$x=200$ but how you did get that 0.75 multiplied by the sale price? I don't understand.

My reasoning went as follows:

Cost + profit = selling price.

Let's abbreviate this by:

$C + P = S$.

If we are given that $P = (0.25)S$, then:

$C = S - P = S - (0.25)S = (1 - 0.25)S = (0.75)S$

If the profit is 25% of the selling price, the other 75% must be the cost.

We are given the cost, and your original post states (correctly) that the selling price is 80% of the marked price (a 20% mark-down).

Personally, in a situation like this, I prefer to use fractions rather than decimals.

EDIT: comparing MarkFL's response and mine, I realized there is an inherent ambiguity in the problem, which is this:

We are told the profit is 25%, but...25% of WHAT, exactly?

If the profit is 25% of the selling price, then my methodology is correct. If the profit is 25% of the cost, then MarkFL's methodology is correct.

MarkFL's profit calculation is based on a profit percentage.

My calculation is based on a profit margin.

I suspect my answer may be what your text is asking for, but without a more complete definition of terms, I cannot be sure.
 
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  • #6
can you show me how to represent the equation using just one variable?

and also why do you equate $0.75(0.8x)=120$
 
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  • #7
We HAVE just one variable, the cost is known to us.
 
  • #8
this is my second try,

let $x=$ marked price; $x−0.2x=$ sale price. then, $0.8x=$ sale price.

Since $C+P=S$ where $C=$ cost, $P=$ profit, and $S=$ sale price.

we know that $C=120$, and $P=0.25(0.8x)$

then I'll have this equation $120+0.25(0.8x)=0.8x$ now $120=0.8x-0.2x$ then $120=0.6x$

so the marked price will be $x=200$ is this correct?
 
  • #9
Deveno is right...the way I viewed it is by letting profit equal revenue minus cost. Since the revenue in this case is the discounted price, I interpreted the problem as meaning this must be 25% of the cost:

Profit = Revenue - Cost

\(\displaystyle 0.25C=D-C\)

\(\displaystyle D=1.25C\)
 

FAQ: Marked Price for 20% Discount Sofa with 25% Profit

1. What is the formula for calculating the marked price for a sofa that has a 20% discount and a 25% profit margin?

The formula for calculating the marked price for a sofa with a 20% discount and a 25% profit margin is: Marked Price = Cost Price x (1 + Profit Margin) x (1 - Discount Percentage)

2. How do I determine the cost price of the sofa if I know the marked price and the discount and profit percentages?

To determine the cost price of the sofa, you can use the following formula: Cost Price = Marked Price / (1 + Profit Margin) / (1 - Discount Percentage)

3. Can the discount and profit percentages be changed to achieve a desired marked price?

Yes, the discount and profit percentages can be changed to achieve a desired marked price. However, the change in one percentage may affect the other. It is important to calculate and adjust both percentages accordingly to achieve the desired marked price.

4. What is the difference between discount and profit percentage?

The discount percentage is the amount by which the marked price is reduced, while the profit percentage is the additional amount added to the cost price to determine the marked price. Essentially, the discount percentage reduces the marked price while the profit percentage increases it.

5. How do I determine the final price of the sofa after the discount and profit have been applied?

To determine the final price of the sofa, subtract the discount percentage from 100% to get the percentage of the marked price. Then, multiply the marked price by this percentage to get the final price after the discount. Next, add the profit percentage to 100% to get the percentage of the final price. Finally, multiply the final price by this percentage to get the final price after the profit has been added.

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