document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1013841>Question 1013841</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a:b =c:d =5:7, find (a+c):(b+d). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #630125 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=630125\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your solution is (a+c)/(b+d) = 5/7.\r<BR>\n" );
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document.write( "you can find it easily by just assuming some values for a and b and c and d and solving.\r<BR>\n" );
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document.write( "you can also find it in terms of a and b and c and d much more arduously by performing algebra on the variables directly.\r<BR>\n" );
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document.write( "in that case you will get (a+c)/(b+d) = (25*(b+d))/(49*(a+c)).\r<BR>\n" );
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document.write( "when you replace a and b and c and d with qualifying numbers, the ratio will wind up being the same, i.e. it will be 5/7.\r<BR>\n" );
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document.write( "first i'll do it using numbers.\r<BR>\n" );
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document.write( "then i'll do it using variables.\r<BR>\n" );
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document.write( "your ratio is a:b = c:d = 5:7.\r<BR>\n" );
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document.write( "this can also be written as a/b = c/d = 5/7\r<BR>\n" );
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document.write( "this means that a/b = 5/7 and that c/d = 5/7.\r<BR>\n" );
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document.write( "if we assume that a is 5 and b is 7, then the ratio is 5/7 for them.\r<BR>\n" );
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document.write( "if we assume that c is 5 and d is 7, then the ratio is 5/7 for them.\r<BR>\n" );
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document.write( "since a = 5 and b = 7 and c = 5 and d = 7, then the ratio of (a+c)/(b+d) becomes (5+5)/(7+7) which becomes 10/14 which simplifies to 5/7.\r<BR>\n" );
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document.write( "you can assume that c = 10 and d = 14, or c = 15 and d = 21.<BR>\n" );
document.write( "as long as the ratio of c/d simplifies to 5/7, all those values are good and will lead to the same conclusion.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "assume a = 5 and b = 7 and c = 15 and d = 21.\r<BR>\n" );
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document.write( "(a+c) = 20<BR>\n" );
document.write( "(b + d) = 28\r<BR>\n" );
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document.write( "(a+c)/(b+d) = 20/28 which simplifies to 5/7.\r<BR>\n" );
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document.write( "with letters it becomes a little more complex, but  you'll get an answer that will be equivalent to the answer that you got with numbers.\r<BR>\n" );
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document.write( "start with a/b = 5/7 and c/d = 5/7\r<BR>\n" );
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document.write( "cross multiply to get 7a = 5b and 7c = 5d\r<BR>\n" );
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document.write( "solve for a to get a = 5b/7<BR>\n" );
document.write( "solve for b to get b = 7a/5<BR>\n" );
document.write( "solve for c to get c = 5d/7<BR>\n" );
document.write( "solve for d to get d = 7c/5\r<BR>\n" );
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document.write( "a+c is equal to 5b/7 + 5d/7 = (5b+5d)/7 = 5(b+d)/7.\r<BR>\n" );
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document.write( "b+d is equal to 7a/5 + 7c/5 = (7a+7c)/5 = 7(a+c)/5.\r<BR>\n" );
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document.write( "(a+c)/(b+d) = 5(b+d)/7 divided by 7(a+c)/5.\r<BR>\n" );
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document.write( "this is equivalent to 5(b+d)/7 times 5/(7(a+c))\r<BR>\n" );
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document.write( "this is equivalent to 5(b+d)*5/ (7*7(a+c))\r<BR>\n" );
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document.write( "simplify further to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%28b%2Bd%29%2F%2849%28a%2Bc%29%29 ALIGN=MIDDLE  ALT=\"25%28b%2Bd%29%2F%2849%28a%2Bc%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "to confirm, we replace a,b,c,d with qualifying values.\r<BR>\n" );
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document.write( "we'll assume a = 5, b = 7, c = 15, d = 21\r<BR>\n" );
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document.write( "the equation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%28b%2Bd%29%2F%2849%28a%2Bc%29%29 ALIGN=MIDDLE  ALT=\"25%28b%2Bd%29%2F%2849%28a%2Bc%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%287%2B21%29%2F%2849%285%2B15%29%29 ALIGN=MIDDLE  ALT=\"25%287%2B21%29%2F%2849%285%2B15%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplify this to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825%2A28%29%2F%2849%2A20%29 ALIGN=MIDDLE  ALT=\"%2825%2A28%29%2F%2849%2A20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "perform the multiplication to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700%2F980 ALIGN=MIDDLE  ALT=\"700%2F980\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when you simplify this, you will find that it is equal to 5/7.\r<BR>\n" );
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