I have worked this several different ways and can not come upwith the answer tha

Question

I have worked this several different ways and can not come upwith the answer that is given in the back of the book which is: setthe original price at $40.00. at 50% off there will be noprofit..
Any help is very appreciated :) thank you for your time, thisis not for homework, I am studying for my final. Thank youagain..
You are the manager of a clothing store and have just purchased 100dress shirts for $20.00 each. After 1 month of selling theshirts at the regular price you plan to have a sale giving 40% offthe original selling price. However, you still want to make aprofit of $4.00 on each shirt at the sale price. What shouldyou price them at initially to insure this? If instead of 40% offat the sale, you give 50% off, by how much is your profit reduced? I have worked this several different ways and can not come upwith the answer that is given in the back of the book which is: setthe original price at $40.00. at 50% off there will be noprofit..
Any help is very appreciated :) thank you for your time, thisis not for homework, I am studying for my final. Thank youagain..

Explanation / Answer

The initial cost to the store is $20*100=$2000 In order to still make a $4 profit then the shirts neet tomake the store the initial cost + $4(quantitiy of shirts). $2000+($4*100)=$2400 at the 40% off sale the shirts new price will be 60% of theoriginal price so... 0.6x=2400 which can be arranged x=2400/0.6 x will be the original price. at the 50% off sale, the original price is divided by 2, whichgives $2000. That is the price the store bought the shirts so thereis no profit. Hope that helps Please rate

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