SOLUTION: a trader sold an article at a discount of 6% for 846. if the article was initially marked to gain 20%. find the market price, cost price of the seller and discount price allowed.

Question 1203463: a trader sold an article at a discount of 6% for 846. if the article was initially marked to gain 20%. find the market price, cost price of the seller and discount price allowed.
Found 4 solutions by josgarithmetic, Theo, ikleyn, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
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a trader sold an article at a discount of 6% for 846.
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The sentence alone, stands on its own.
w, the traders article's initial value before selling it

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This part totally not clear:
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if the article was initially marked to gain 20%. find the market price, cost price of the seller and discount price allowed.
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Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
final sale price was 846 at a discount of 6%.
formula for this was 846 = x - 1.06 * x.
simplify to get 846 = .94 * x
solve for x to get x = 846 / .94 = 900.

the original price was 900, before the 6% discount was applied.

the article was originally marked to give a 20% profit over the cost.

if y = the cost, the original price was set at y * 1.20.
this was designed to give the 20% profit.

since the original price was 900, you get 900 = 1.20 * x.
solve for x to get x = 900 / 1.2 = 750.

you get:

market price = 900
cost price = 750
discount price allowed = 846.

Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.
A trader sold an article at a discount of 6% for 846. If the article was initially marked to gain 20%,
find the market price, cost price of the seller and discount price allowed.
~~~~~~~~~~~~~~~~~~~~~~~~~

My point of view is that this post uses wrong terminology;
therefore, it is not possible to understand the meaning of the problem,
so, this formulation is a kind of gibberish (if to call the things by their proper names).

Below I will write a correct formulation and a solution to modified version,
but before I'd like to give preliminary explanations.

In this problem, the situation is considered from the point of view of the trader.
From this point of view, the following notions/conceptions do work and are applicable:

    - buying price, at which a trader buys an article somewhere outside;
    - marked price, which is written and attached to the article in the store;
    - selling price is for how much a trader sells an article after discount.

Now a correct formulation to the problem is THIS:

A trader sold an article at a discount of 6% for 846. If the article was initially marked to gain 20%, find the marked price, buying price of the trader and discount allowed.

                                The solution is as follows:

Let x be the marked price. Then from the problem x - 0.06x = 846, which implies 0.94x = 846, x = = 900. Thus the marked price is 900 monetary units. Next, the marked price provides 20% profit over the buying price. It gives us this equation 1.2*y = 900, where y is the buying price for the trader. It implies y = = 750. Thus the buying price is 750 monetary units. And finally, the discount allowed is 6% of the marked price, or 0.06*900 = 54 monetary units. ANSWER. Marked price is 900. Buying price is 750. The discount allowed is 54.

Solved.

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In this problem, if to formulate it properly, there is no any " market " price.

There is " marked " price, instead, which is totally different conception.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

a trader sold an article at a discount of 6% for 846. if the article was initially marked to gain 20%. find the market price, cost price of the seller and discount price allowed. As a 6% discount was allowed, SELLING price = 1 - .06 = .94, or 94% With marked price being M, we get the following PROPORTION: .94M = 846 ----- Cross-multiplying Marked price, or Marked price: $900 Discounted price: $846 Discount: $900 - $846 = $54 The marked price ($900) included a 20% gain, so marked price = 1 + .2 = 1.2 Let cost price be C With marked price ($900), being 1.2, we get the following PROPORTION: 1.2C = 900 ----- Cross-multiplying Cost price, or

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