document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1006861>Question 1006861</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi. I am facing problem in this word problem. It is quadratic equation.\r<BR>\n" );
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document.write( "In may 1994 Mr Chauhan changed 1140 Indian Rupees into German Marks when the rate of exchange was x rupees =1 Mark. <BR>\n" );
document.write( "(a) write down an expression in terms of x , for the number of Marks he received\r<BR>\n" );
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document.write( "In july, Mr Chuhan again changed 1140 rupees into Marks. The rate of exchange was then (x+1) rupees=1 Mark<BR>\n" );
document.write( "(b) write down an expression in term of x, for the number of Marks he received this time,<BR>\n" );
document.write( "(c)Given that he received 3 Marks less in July than he did in May, form an equasion in x and show that it reduces to    x^2 +x-380=0<BR>\n" );
document.write( "(d) Solve this equation to find the rate of exchange in May 1994.<BR>\n" );
document.write( "Thank you for reading my question. Please reply. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #622934 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=622934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here goes.\r<BR>\n" );
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document.write( "in may the ratio of rupees to marks is x to 1 = x/1.\r<BR>\n" );
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document.write( "in july the ratio of rupees to marks is (x+1) to 1 = (x+1)/1.\r<BR>\n" );
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document.write( "he exchanged 1140 rupees to marks in both months.\r<BR>\n" );
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document.write( "in may, the ratio becomes 1140/m = x/1.\r<BR>\n" );
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document.write( "in july, the ratio becomes 1140/m = (x+1)/1.\r<BR>\n" );
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document.write( "solve each of these equations for m to get:\r<BR>\n" );
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document.write( "in may, m = 1140/x.\r<BR>\n" );
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document.write( "in july, m = 1140/(x+1).\r<BR>\n" );
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document.write( "to distinguish the marks between may and july, we'll call m in may m1 and we'll call m in july m2.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "m1 = 1140/x.\r<BR>\n" );
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document.write( "m2 = 1140/(x+1)\r<BR>\n" );
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document.write( "you are given that the number of marks in july is equal to the number of marks in may less 3.\r<BR>\n" );
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document.write( "that means that m2 = m1 - 3.\r<BR>\n" );
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document.write( "since m2 = 1140/(x+1) and m1 = 1140/x, you get:\r<BR>\n" );
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document.write( "m2 = m1 - 3 becomes:\r<BR>\n" );
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document.write( "1140/(x+1) = 1140/x - 3.\r<BR>\n" );
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document.write( "multiply both sides of this equation by (x+1)*(x) and you get:\r<BR>\n" );
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document.write( "1140/(x+1)*(x)*(x+1) = 1140/x*(x)*(x+1) - 3*(x)*(x+1) which results in:\r<BR>\n" );
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document.write( "1140*x = 1140*(x+1) - 3*(x)*(x+1) which can be further simplified to:\r<BR>\n" );
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document.write( "1140x = 1140x + 1140 - 3x^2 - 3x.\r<BR>\n" );
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document.write( "if you subtract 1140x from both sides of this equation, you get:\r<BR>\n" );
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document.write( "0 = 1140 - 3x^2 - 3x\r<BR>\n" );
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document.write( "multiply both sides of this equation by -1 and you get:\r<BR>\n" );
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document.write( "0 = -1140 + 3x^2 + 3x\r<BR>\n" );
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document.write( "divide both sides of this equation by 3 and you get:\r<BR>\n" );
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document.write( "0 = -380 + x^2 + x\r<BR>\n" );
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document.write( "reorder the terms of the expression on the right in descending order of degree to get:\r<BR>\n" );
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document.write( "0 = x^2 + x - 380\r<BR>\n" );
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document.write( "by the law of commutivity of equations (if a = b, then b = a), this is the same as:\r<BR>\n" );
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document.write( "x^2 + x - 380 = 0.\r<BR>\n" );
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document.write( "that matches the equation that you showed in statement c.\r<BR>\n" );
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document.write( "factor this equation to get:\r<BR>\n" );
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document.write( "(x+20)*(x-19) = 0\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 20 or x = 19.\r<BR>\n" );
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document.write( "x can't be negative, so x has to be 19.\r<BR>\n" );
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document.write( "replace x in the original equation with 19 to get:\r<BR>\n" );
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document.write( "m1 = 1140/19 = 60\r<BR>\n" );
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document.write( "m2 = 1140/20 = 57\r<BR>\n" );
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document.write( "m2 - m1 = -3 which is correct since there are 3 less marks in july than in may.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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