document.write( "Question 92341: I am printing a sticker.
\n" ); document.write( "The width of the sticker = 280cm
\n" ); document.write( "The height of the sticker = 254cm
\n" ); document.write( "The no. of meter² of the sticker = 2.8 X 2.54 = 7.112 meter²
\n" ); document.write( "If 7.112 meter² at $55/meter² cost $391.16 to produce,
\n" ); document.write( "how much do I need to reduce the width and height of the sticker so that a
\n" ); document.write( "total cost of $245 will be charged to the client buying the sticker?
\n" ); document.write( "You need to keep the width vs height proportionate so that they are both
\n" ); document.write( "reduced proportionally.
\n" ); document.write( ":-)
\n" ); document.write( "Good luck!
\n" ); document.write( "Patrick A.
\n" ); document.write( "PS I need a general formula please so that I can apply it to the rest of the
\n" ); document.write( "dimensions of stickers which I am producing, and for which I need to reduce
\n" ); document.write( "their cost. \n" ); document.write( "

Algebra.Com's Answer #67197 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "I am printing a sticker.\r\n" );
document.write( "The width of the sticker = 280cm\r\n" );
document.write( "The height of the sticker = 254cm\r\n" );
document.write( "The no. of meter² of the sticker = 2.8 X 2.54 = 7.112 meter²\r\n" );
document.write( "If 7.112 meter² at $55/meter² cost $391.16 to produce,\r\n" );
document.write( "how much do I need to reduce the width and height of the sticker so that a\r\n" );
document.write( "total cost of $245 will be charged to the client buying the sticker?\r\n" );
document.write( "You need to keep the width vs height proportionate so that they are both\r\n" );
document.write( "reduced proportionally.\r\n" );
document.write( ":-)\r\n" );
document.write( "Good luck!\r\n" );
document.write( "Patrick A. \r\n" );
document.write( "PS I need a general formula please so that I can apply it to the rest of the\r\n" );
document.write( "dimensions of stickers which I am producing, and for which I need to reduce\r\n" );
document.write( "their cost.\r\n" );
document.write( "\r\n" );
document.write( "Since you want a general formula, let's reword the problem with\r\n" );
document.write( "unknown constants instead of known values, and, to make it easier,\r\n" );
document.write( "keep all units in meters and meters²:\r\n" );
document.write( "\r\n" );
document.write( "Rewording with unknown constants\r\n" );
document.write( "\r\n" );
document.write( "I am printing a sticker.\r\n" );
document.write( "The width of the sticker = W meters\r\n" );
document.write( "The height of the sticker = H meters\r\n" );
document.write( "The area of the sticker = W times H = WH meter² \r\n" );
document.write( "At $M/meter², the cost is $WHM to produce,\r\n" );
document.write( "how much do I need to reduce the width and height of the sticker so \r\n" );
document.write( "that a total cost of $C will be charged to the client buying the \r\n" );
document.write( "sticker?\r\n" );
document.write( "\r\n" );
document.write( ">>...The (old) width of the sticker = W...<<\r\n" );
document.write( ">>...The (old) height of the sticker = H...<<\r\n" );
document.write( "\r\n" );
document.write( "Let x = the number (which will be less than one) by which we must\r\n" );
document.write( "multiply both the base and the height.\r\n" );
document.write( "\r\n" );
document.write( "(The new width) = (The old width times x) = Wx\r\n" );
document.write( "(The new height) = (The old height times x) = Hx\r\n" );
document.write( "(The new area) = (The new width tmes the new height) = (Wx)(Hx) = WHx² meter². \r\n" );
document.write( "\r\n" );
document.write( ">>...$M/meter²...<< \r\n" );
document.write( "\r\n" );
document.write( "(Cost of new area) = (New area times $M) = (WHx²)(M) = WHMx²\r\n" );
document.write( "\r\n" );
document.write( "We want (Cost of new area) to equal $C, so we set\r\n" );
document.write( "\r\n" );
document.write( "WHMx² = C\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by WHM\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( "Take square root of both sides:\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( "That's the general formula for the number to multiply\r\n" );
document.write( "both the width W and the height H by to reduce the cost from\r\n" );
document.write( "$WHM to $C, where $M is the price per square meter.\r\n" );
document.write( "\r\n" );
document.write( "However, we must answer the question:\r\n" );
document.write( "\r\n" );
document.write( ">>...how much do I need to reduce the width and height of the sticker...<< \r\n" );
document.write( "\r\n" );
document.write( "We must reduce the width from W meters to xW meters, so that means we must\r\n" );
document.write( "reduce the width by (W - xW) meters or by W(1-x) meters.\r\n" );
document.write( "\r\n" );
document.write( "We must reduce the heigth from H meters to xH meters, so that means we must\r\n" );
document.write( "reduce the height by (H - xH) meters or by H(1-x) meters.\r\n" );
document.write( "\r\n" );
document.write( "So for this problem, we substitute W = 280cm = 2.8m, H = 254cm = 2.54m,\r\n" );
document.write( "M = $55, C = $245\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
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document.write( " = .7914178174\r\n" );
document.write( "\r\n" );
document.write( "We must reduce the width from W meters to xW meters, so we must reduce\r\n" );
document.write( "the width by (W - xW) meters or by W(1-x) meters.\r\n" );
document.write( "\r\n" );
document.write( "We must reduce the width from 2.8 meters to (.7914178174)2.8 or \r\n" );
document.write( "2.215969889 meters, so we must reduce the width by (2.8 - 2.215969889) \r\n" );
document.write( "meters or by .584030111 meters, or about 58.4 centimeters. \r\n" );
document.write( "\r\n" );
document.write( "We must reduce the height from H meters to xH meters, so we must reduce\r\n" );
document.write( "the height by (H - xH) meters or by H(1-x) meters.\r\n" );
document.write( "\r\n" );
document.write( "We must reduce the height from 2.54 meters to (.7914178174)2.54 or\r\n" );
document.write( "2.010201256 meters, so we must reduce the height by (2.54 - 2.010201256) \r\n" );
document.write( "meters or by .5297987437 meters, or about 53.0 centimeters.\r\n" );
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document.write( "Edwin

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