document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1124209>Question 1124209</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two numbers are in the ratio 2:5. if their difference is 48,what is the bigger number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #740555 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=740555\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> two numbers are in the ratio of 2:5.<BR>\n" );
document.write( "their difference is 48.<BR>\n" );
document.write( "what is the bigger of the two numbers?\r<BR>\n" );
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document.write( "let the numbers be A and B.<BR>\n" );
document.write( "let the ratio be A:B = 2:5<BR>\n" );
document.write( "this can also be written at A/B = 2/5\r<BR>\n" );
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document.write( "solve for A to get A = 2/5 * B<BR>\n" );
document.write( "this makes B the larger number.\r<BR>\n" );
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document.write( "therefore B - A = 48\r<BR>\n" );
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document.write( "solve for B to get B = A + 48\r<BR>\n" );
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document.write( "you have A = 2/5 * B and you have B = A + 48\r<BR>\n" );
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document.write( "replace B in the first equation with its equivalent value of A + 48 from the second equation to get:\r<BR>\n" );
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document.write( "A = 2/5 * B becomes A = 2/5 * (A + 48)<BR>\n" );
document.write( "simplify to get A = 2/5 * A + 2/5 * 48<BR>\n" );
document.write( "subtract 2/5 * A from both sides of this equation to get:<BR>\n" );
document.write( "A - 2/5 * A = 2/5 * 48<BR>\n" );
document.write( "combine like terms to get 3/5 * A = 2/5 * 48<BR>\n" );
document.write( "multiply both sides of this equation by 5/3 to get:<BR>\n" );
document.write( "5/3 * 3/5 * A = 5/3 * 2/5 * 48<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "A = 10/15 * 48<BR>\n" );
document.write( "solve for A to get A = 32\r<BR>\n" );
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document.write( "you have A = 32 and B = 80\r<BR>\n" );
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document.write( "B = A + 48 gets you B = 32 + 48 = 80\r<BR>\n" );
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document.write( "A/B = 2/5 becomes 32/80 = 2/5 <BR>\n" );
document.write( "divide 32 by 16 to get 2 and divide 80 by 16 to get 5.<BR>\n" );
document.write( "this means that 32/80 is equivalent to 2/5 which means the ratio of A/B is correct.\r<BR>\n" );
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document.write( "you could also confirm by cross multiplying.<BR>\n" );
document.write( "cross multiply 2/5 = 32/80 to get 160 = 160, confirming the ratios are equivalent.\r<BR>\n" );
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document.write( "your solution is that the bigger number is 80.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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