document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=919327>Question 919327</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cha Cruz has a garden. The ratio of roses to tulips is 2 : 5, the ratio of roses to orchids is 7 : 6. Cha Cruz<BR>\n" );
document.write( "      wonders what the ratio of tulips to orchids is. If Cha Cruz has 183 plants, how many of each kind are there?<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 #557642 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=557642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the ratio of roses to tulips is 2/5.<BR>\n" );
document.write( "this means that you have 2 roses for every 5 tulips.<BR>\n" );
document.write( "this also means you have 5 tulips for every 2 roses.\r<BR>\n" );
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document.write( "the ratio of roses to orchids is 7/6.<BR>\n" );
document.write( "this means you have 7 roses for every 6 orchids.<BR>\n" );
document.write( "this also means you have 6 orchids for every 7 roses.\r<BR>\n" );
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document.write( "you want to find the ratio of tulips to orchards.\r<BR>\n" );
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document.write( "since you know the ratio of roses to orchids, then find the equivalent number of tulips for every rose and you have your answer.\r<BR>\n" );
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document.write( "2 roses for every 5 tulips means that you have 5 tulips for every 2 roses which means that you have 5/2 tulips for every rose.\r<BR>\n" );
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document.write( "you can replace one rose with 5/2 tulips in your ratio of 7 roses to every 6 orchids.\r<BR>\n" );
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document.write( "the ratio of roses to orchids is equal to 7/6.<BR>\n" );
document.write( "multiply 7 roses by 5/2 tulips for each rose and you get 35/2 tulips for every 6 orchids.<BR>\n" );
document.write( "your ratio of 7 roses to 6 orchids becomes 35/2 tulips for every 6 orchids.<BR>\n" );
document.write( "35/2 divided by 6 is equal to 35/2 * 1/6 which is equal to 35 / 12.<BR>\n" );
document.write( "your ratio of tulips to orchids is therefore equal to 35/12.\r<BR>\n" );
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document.write( "you have the following ratios;\r<BR>\n" );
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document.write( "roses to tulips = 2/5<BR>\n" );
document.write( "roses to orchids = 7/6<BR>\n" );
document.write( "tulips to orchids = 35/12.\r<BR>\n" );
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document.write( "there are 183 plants in total.\r<BR>\n" );
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document.write( "let r = number of roses.<BR>\n" );
document.write( "let t = number of tulips.<BR>\n" );
document.write( "let o = number of orchids.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "r + t + o = 183\r<BR>\n" );
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document.write( "since r = 2/5 * t, this means that t = 5/2 * r and you can replace t in the equation with 5/2 * r to get:\r<BR>\n" );
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document.write( "r + 5/2 * r + o = 183.\r<BR>\n" );
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document.write( "since r = 7/6 * o, this means that o = 6/7 * r and you can replace o in the equation with 6/7 * r to get:\r<BR>\n" );
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document.write( "r + 5/2 * r + 6/7 * r = 183.\r<BR>\n" );
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document.write( "you can now solve for r in the equation to get r = 42.\r<BR>\n" );
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document.write( "when r = 42, t = 5/2 * r = 5/2 * 42 = 105.\r<BR>\n" );
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document.write( "when r = 42, o = 6/7 * r = 6/7 * 42 = 36.\r<BR>\n" );
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document.write( "you will have 42 roses and 105 tulips and 36 orchids.\r<BR>\n" );
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document.write( "those are your solutions.<BR>\n" );
document.write( "the ratio of tulips to orchids is 35/12.<BR>\n" );
document.write( "if the total number of flowers is 183, then you have:\<BR>\n" );
document.write( "42 roses<BR>\n" );
document.write( "105 tulips<BR>\n" );
document.write( "36 orchids\r<BR>\n" );
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