document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090120>Question 1090120</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sorry I don't know which type it is.<BR>\n" );
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document.write( "It is given that the ratio of two numbers is 3:7. If 6 is subtracted from both numbers, their ratio will become 1:3. What is the ratio of number if 6 is added to both numbers?<BR>\n" );
document.write( "Thank you very much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704517 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=704517\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the ratio of 2 numbers is 3:7 which can be shown as 3/7.\r<BR>\n" );
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document.write( "let x be the first number and y be the second number.\r<BR>\n" );
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document.write( "you get x/y = 3/7\r<BR>\n" );
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document.write( "if 6 is subtracted from both numbers, their ration becomes 1/3.\r<BR>\n" );
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document.write( "you get (x-6)/(y-6) = 1/3\r<BR>\n" );
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document.write( "solve for x in each of these equations.\r<BR>\n" );
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document.write( "start with x/y = 3/7<BR>\n" );
document.write( "multiply both sides by y to get x = 3/7 * y\r<BR>\n" );
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document.write( "start with (x-6)/(y-6) = 1/3<BR>\n" );
document.write( "multiply by (y-6) to get x-6 = 1/3 * (y-6)<BR>\n" );
document.write( "add 6 to both sides to get x = 1/3 * (y-6) + 6\r<BR>\n" );
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document.write( "since both expressions are equal to x, you can set them equal to each other to get:\r<BR>\n" );
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document.write( "3/7 * y = 1/3 * (y-6) + 6\r<BR>\n" );
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document.write( "simplify the expression on the right to get:\r<BR>\n" );
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document.write( "3/7 * y = 1/3 * y - 6/3 + 6\r<BR>\n" );
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document.write( "multiply both sides of this equation by 21 to get:\r<BR>\n" );
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document.write( "21 * 3/7 * y = 21 * 1/3 * y - 21 * 6/3 + 21 * 6\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "9 * y = 7 * y - 42 + 126\r<BR>\n" );
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document.write( "subtract 7 * y from both sides of and combine like terms to get:\r<BR>\n" );
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document.write( "2 * y = 84\r<BR>\n" );
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document.write( "solve for y to get y = 42.\r<BR>\n" );
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document.write( "when y = 42, the equation of x = 3/7 * y becomes x = 3/7 * 42 which becomes x = 18.\r<BR>\n" );
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document.write( "you have x = 18 and y = 42.\r<BR>\n" );
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document.write( "therefore x/y = 18/42 which simplifies to 3/7.\r<BR>\n" );
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document.write( "likewise (18-6) / (42-6) becomes 12/36 which simplifies to 1/3.\r<BR>\n" );
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document.write( "likewise (18+6) / (42+6) becomes 24/48 which simplifies to 1/2.\r<BR>\n" );
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document.write( "looks like the solution is good.\r<BR>\n" );
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document.write( "the solution is x = 18 and y = 42.\r<BR>\n" );
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document.write( "i'm sorry.\r<BR>\n" );
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document.write( "that's not the solution.\r<BR>\n" );
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document.write( "it's an intermediate result.\r<BR>\n" );
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document.write( "the problem asks for the ratio if 6 is added to both numbers.\r<BR>\n" );
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document.write( "that solution is 1/2.\r<BR>\n" );
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