document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=875833>Question 875833</A>: <I><SPAN STYLE=\"word-break: break-all;\"> leela sold her car seat covers at a profit of 7%. if she had sold it for $4.25 more, she would have got 10% profit. how much did leela sell her seat covers for?\r<BR>\n" );
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document.write( "With working out please.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #528431 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=528431\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we let s = sale price of the item and c = cost of the item and p = profit of the item.\r<BR>\n" );
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document.write( "at 7% profit, our first equation becomes:\r<BR>\n" );
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document.write( "p = s - c\r<BR>\n" );
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document.write( "since profit is equal to 7% of the cost, we also get:\r<BR>\n" );
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document.write( "p = .07*c\r<BR>\n" );
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document.write( "when we replace p with it's equivalent expression of .07*c, our equation becomes:\r<BR>\n" );
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document.write( ".07*c = s - c\r<BR>\n" );
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document.write( "if we solve for s, we will get:\r<BR>\n" );
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document.write( "s = 1.07*c ***** see note 1 at the bottom on how to derive this.\r<BR>\n" );
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document.write( "our second equation is:\r<BR>\n" );
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document.write( "p = s + 4.25 - c\r<BR>\n" );
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document.write( "since p is also equal to .10*c in this equation, then this equation becomes:\r<BR>\n" );
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document.write( ".10*c = s + 4.25 - c\r<BR>\n" );
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document.write( "if we solve for s, we will get: \r<BR>\n" );
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document.write( "s = 1.10*c - 4.25 ***** see note 2 at the bottom on how to derive this.\r<BR>\n" );
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document.write( "we now have two equations that are both equal to s.<BR>\n" );
document.write( "s is the original selling price.<BR>\n" );
document.write( "the equations are:\r<BR>\n" );
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document.write( "s = 1.07*c<BR>\n" );
document.write( "s = 1.10*c - 4.25\r<BR>\n" );
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document.write( "since s = 1.07*c in the first equation, we can replace s with its equivalent expression of 1.07*c in the second equation to get:\r<BR>\n" );
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document.write( "1.07*c = 1.10*c - 4.25\r<BR>\n" );
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document.write( "solve for c in this equation to get:\r<BR>\n" );
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document.write( "c = 4.25 / .03 ***** see note 3 at the bottom on how to derive this.\r<BR>\n" );
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document.write( "solve for c to get:\r<BR>\n" );
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document.write( "c = 141.66667 rounded to 5 decimal places.\r<BR>\n" );
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document.write( "since c is equal to the cost of the item, we now know what the cost is and we can proceed to solve the rest of the problem.\r<BR>\n" );
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document.write( "our first equation was .07*c = s - c\r<BR>\n" );
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document.write( "we solved for s to get 1.07*c = s ***** see note 1 at the bottom on how this was derived.\r<BR>\n" );
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document.write( "since c = 141.66667, we can solve for s to get:\r<BR>\n" );
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document.write( "s = 1.07*141.66667 which is equal to 151.583337 rounded to 5 decimal places.\r<BR>\n" );
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document.write( "if we add 4.25 to this, we will get a sale price of 155.83337 rounded to 5 decimal places.\r<BR>\n" );
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document.write( "151.583337 represents the original sale price at 7% profit.\r<BR>\n" );
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document.write( "155.83337 represents the new sale price after we add 4.25 to the original sale price.\r<BR>\n" );
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document.write( "p = s - c with the new sale price and the original cost becomes:\r<BR>\n" );
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document.write( "p = 155.83337 - 141.66667 = 14.1667\r<BR>\n" );
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document.write( "that's our new profit after we added 4.25 to the original sale price.\r<BR>\n" );
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document.write( "rate of profit = p / c = 14.1667 / 141.66667 = .10000 rounded to 5 decimal places.\r<BR>\n" );
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document.write( "that's a 10% profit using the new sale price, so we solved the problem correctly.\r<BR>\n" );
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document.write( "the answer to the question is:\r<BR>\n" );
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document.write( "leela sold her seat covers for $151.58 rounded to 2 decimal places.\r<BR>\n" );
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document.write( "That's the selling price at 7% profit.\r<BR>\n" );
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document.write( "notes are below:\r<BR>\n" );
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document.write( "***** note 1\r<BR>\n" );
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document.write( "start with:<BR>\n" );
document.write( ".07*c = s - c<BR>\n" );
document.write( "add c to both sides of this equation to get:<BR>\n" );
document.write( "c + .07*c = s<BR>\n" );
document.write( "factor out the c on the left side of this equation to get:<BR>\n" );
document.write( "(1 + .07)*c = s<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "1.07*c = s<BR>\n" );
document.write( "that's the same as:<BR>\n" );
document.write( "s = 1.07*c\r<BR>\n" );
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document.write( "***** note 2\r<BR>\n" );
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document.write( "start with:<BR>\n" );
document.write( ".10*c = s + 4.25 - c<BR>\n" );
document.write( "add c to both sides of this equation and subtract 4.25 from both sides of this equation to get:<BR>\n" );
document.write( "c + .10*c - 4.25 = s<BR>\n" );
document.write( "factor out the c on the left side of the equation to get:<BR>\n" );
document.write( "(1 + .07)*c - 4.25 = s<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "1.10*c - 4.25 = s<BR>\n" );
document.write( "that's the same as:<BR>\n" );
document.write( "s = 1.10*c - 4.25\r<BR>\n" );
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document.write( "***** note 3\r<BR>\n" );
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document.write( "start with:<BR>\n" );
document.write( "1.07*c = 1.10*c - 4.25<BR>\n" );
document.write( "subtract 1.07*c from both sides of this equation and add 4.25 to both sides of this equation to get:<BR>\n" );
document.write( "4.25 = 1.10*c - 1.07*c<BR>\n" );
document.write( "factor out the c on the right side of this equation to get:<BR>\n" );
document.write( "4.25 = (1.10-1.07)*c<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "4.25 = .03*c<BR>\n" );
document.write( "divide both sides of this equation by .03 to get:<BR>\n" );
document.write( "4.25/.03 = c<BR>\n" );
document.write( "that's the same as:<BR>\n" );
document.write( "c = 4.25 / .03\r<BR>\n" );
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