document.write( "Question 1145178: A company makes t-shirts and their research shows that that price and demand are related linearly:p=mx+b.They know that in order to sell 5 shirts they need to set the price at $37, and in order to sell 15 shirts they need to set the price at $17. Find the linear equation relating price to demand.
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Algebra.Com's Answer #766384 by ikleyn(52835) $\"\"$ $\"About$

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document.write( "The demand function is the number of sold items as a function of price.\r\n" );
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document.write( "The slope of the demand function is the ratio of the increment of the number of the sold items to the increment of the price.\r\n" );
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document.write( "In this case, the increment of the number of the sold items is  5 - 15 = -10  and \r\n" );
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document.write( "              the increment of the price is  37-17 = 20 dollars.\r\n" );
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document.write( "Therefore, the slope is   = -0.5 item per dollar.\r\n" );
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document.write( "Hence, the requested demand function is  d(p) = 5 - 0.5*(p-37).    (1)\r\n" );
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document.write( "CHECK.  At p = 37,  d(p) = d(37) = 5 - 0.5*(37-37) = 5 - 0.5*0 = 5 - 0 = 5 items.   ! Correct !\r\n" );
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document.write( "        At p = 17,  d(p) = d(17) = 5 - 0.5*(17-37) = 5 - 0.5*(-20) = 5 + 0.5*20 = 5 + 10 = 15 items.   ! Correct !  \r\n" );
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