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Profit Problems

paulmdrdo

Active member
May 13, 2013
386
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

Well-known member
MHB Math Scholar
Feb 15, 2012
1,967
Re: profit problems

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

$0.75(0.8x) = 120$?
 

paulmdrdo

Active member
May 13, 2013
386
Re: profit problems

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

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
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

Well-known member
MHB Math Scholar
Feb 15, 2012
1,967
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.
 
Last edited:

paulmdrdo

Active member
May 13, 2013
386
can you show me how to represent the equation using just one variable?

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

Deveno

Well-known member
MHB Math Scholar
Feb 15, 2012
1,967
We HAVE just one variable, the cost is known to us.
 

paulmdrdo

Active member
May 13, 2013
386
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

Administrator
Staff member
Feb 24, 2012
13,775
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

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

\(\displaystyle D=1.25C\)