document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207784>Question 1207784</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are the manager of a clothing store and have just purchased 100 dress shirts for $20.00 each. After 1 month of selling the shirts at the regular price, you plan to have a sale giving 40% off the original selling price. However,you still want to make a profit of $4 on each shirt at the sale price.What should you price the shirts at initially to ensure this? If, instead of 40% off at the sale, you give 50% off, by how much is your profit reduced? </SPAN>\n" );
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document.write( "x = initial price<BR>\n" );
document.write( "0.40x = discount value = amount saved for the customer<BR>\n" );
document.write( "x - 0.40x = 0.60x = sale price<BR>\n" );
document.write( "0.60x - 20 = profit per shirt = 4 dollars\r<BR>\n" );
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document.write( "0.60x - 20 = 4<BR>\n" );
document.write( "0.60x = 4+20<BR>\n" );
document.write( "0.60x = 24<BR>\n" );
document.write( "x = 24/0.60<BR>\n" );
document.write( "x = 40<BR>\n" );
document.write( "The initial price should be <font color=red>$40</font>.\r<BR>\n" );
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document.write( "If that's the case then 40% of $40 = 0.40*40 = 16 dollars is saved and the sale price would be 40-16 = 24 dollars (or 60% of 40 = 0.60*40 = 24).<BR>\n" );
document.write( "Then profit per shirt = price-cost = 24-20 = 4 dollars.<BR>\n" );
document.write( "We have confirmed $40 is the correct starting price.\r<BR>\n" );
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document.write( "Now consider a 50% discount.<BR>\n" );
document.write( "The customer saves 0.50*40 = 20 dollars.<BR>\n" );
document.write( "The sale price is 40-20 = $20<BR>\n" );
document.write( "The profit per shirt is $0 since price-cost = 20-20 = 0.<BR>\n" );
document.write( "The manager doesn't gain any money, nor loses money. The manager breaks even.<BR>\n" );
document.write( "The old profit $4 dropped to $0, so the profit reduced by <font color=red>$4</font>.\r<BR>\n" );
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document.write( "-----------------------------------------------------------\r<BR>\n" );
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document.write( "Summary:\r<BR>\n" );
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document.write( "Initial price should be <font color=red>$40</font><BR>\n" );
document.write( "Profit is reduced by <font color=red>$4</font> if you give a 50% discount instead of a 40% discount.<BR>\n" );
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