Marked Price for 20% Discount Sofa with 25% Profit

[paulmdrdo1]

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.

 

[Deveno]

Re: profit problems

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

$0.75(0.8x) = 120$?

 

[paulmdrdo1]

Re: profit problems

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

 

[MarkFL]

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?

 

[Deveno]

Re: profit problems

$x=200$ 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.

 

[paulmdrdo1]

can you show me how to represent the equation using just one variable?

and also why do you equate $0.75(0.8x)=120$

 

[Deveno]

We HAVE just one variable, the cost is known to us.

 

[paulmdrdo1]

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?

 

[MarkFL]

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

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

\(\displaystyle D=1.25C\)