document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119941>Question 1119941</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I go about solving this ratio problem?\r<BR>\n" );
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document.write( "Jay and Raymond bought some cookies in the ratio 3:5. After Raymond bought another 24 cookies, the ratio became 1:2. How many cookies did Jay buy?\r<BR>\n" );
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document.write( "Thanks in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #735568 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=735568\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> j is the number of cookies that jay has.<BR>\n" );
document.write( "r is the number of cookies that raymond has.\r<BR>\n" );
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document.write( "the ratio of the number of jay's cookies to raymond's cookies is 3/5.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "j/r = 3/5\r<BR>\n" );
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document.write( "when raymond buys another 24 cookies, the ratio becomes 1/2.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "j/(r+24) = 1/2.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "j/r = 3/5.\r<BR>\n" );
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document.write( "j/(r+24) = 1/2\r<BR>\n" );
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document.write( "these 2 equations need to be solved simultaneously.\r<BR>\n" );
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document.write( "multiply both sides of the first equation by 5r to get:\r<BR>\n" );
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document.write( "j/r = 3/5 becomes 5j = 3r.\r<BR>\n" );
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document.write( "subtract 3r from both sides of this equation to get:\r<BR>\n" );
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document.write( "5j - 3r = 0\r<BR>\n" );
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document.write( "multiply both sides of the second equation by 2 * (r+24) to get:\r<BR>\n" );
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document.write( "j/(r+24) = 1/2 becomes 2j = r+24\r<BR>\n" );
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document.write( "subtract r from both sides of this equation to get:\r<BR>\n" );
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document.write( "2j - r = 24\r<BR>\n" );
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document.write( "the two equations that need to be solved simultaneously are now:\r<BR>\n" );
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document.write( "5j - 3r = 0<BR>\n" );
document.write( "2j - r = 24\r<BR>\n" );
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document.write( "multiply both sides of the second equation by 3 and leave the first equation as is to get:\r<BR>\n" );
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document.write( "5j - 3r = 0<BR>\n" );
document.write( "6j - 3r = 72\r<BR>\n" );
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document.write( "subtract the first equation from the second to get:\r<BR>\n" );
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document.write( "j = 72\r<BR>\n" );
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document.write( "go back to the first original equation of j/r = 3/5 and replace j with 72 to get:\r<BR>\n" );
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document.write( "j/r = 3/5 becomes 72/r = 3/5\r<BR>\n" );
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document.write( "solve for r to get r = 72 * 5 / 3 = 120.\r<BR>\n" );
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document.write( "you now have:\r<BR>\n" );
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document.write( "j = 72<BR>\n" );
document.write( "r = 120\r<BR>\n" );
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document.write( "j/r = 72 / 120.\r<BR>\n" );
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document.write( "divide numerator and denominator of this equation by 24 to get:\r<BR>\n" );
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document.write( "j/r = 3/5.\r<BR>\n" );
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document.write( "first ratio is correct when j = 72 and r = 120.\r<BR>\n" );
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document.write( "second original equation is j/(r+24) = 1/2.\r<BR>\n" );
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document.write( "replace j with 72 and r with 120 to get:\r<BR>\n" );
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document.write( "72/(120 + 24) = 1/2 becomes 72/144 = 1/2 which becomes 1/2 = 1/2 when 72/144 numerator and denominator are both divided by 72.\r<BR>\n" );
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document.write( "solution looks good.\r<BR>\n" );
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document.write( "number of cookies that jay had originally are 72.\r<BR>\n" );
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document.write( "number of cookies that raymond had originally are 120.\r<BR>\n" );
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document.write( "solution is jay bought 72 cookies.\r<BR>\n" );
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document.write( "another way to solve this is as shown below.\r<BR>\n" );
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document.write( "2 original equations are:\r<BR>\n" );
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document.write( "j/r = 3/5.<BR>\n" );
document.write( "j/(r+24) = 1/2\r<BR>\n" );
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document.write( "solve for j in both equations to get:\r<BR>\n" );
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document.write( "j = 3/5 * r<BR>\n" );
document.write( "j = 1/2 * (r + 24)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "j = 3/5 * r<BR>\n" );
document.write( "j = 1/2 * r + 1/2 * 24\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "j = 3/5 * r<BR>\n" );
document.write( "j = 1/2 * r + 12\r<BR>\n" );
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document.write( "since j is equal to both, then both are equal to each other and you get:\r<BR>\n" );
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document.write( "3/5 * r = 1/2 * r + 12\r<BR>\n" );
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document.write( "subtract 1/2 * r from both sides of this equation to get:\r<BR>\n" );
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document.write( "3/5 * r - 1/2 * r = 12\r<BR>\n" );
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document.write( "multiply both sides of this equation by 10 to get:\r<BR>\n" );
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document.write( "6 * r - 5 * r = 120\r<BR>\n" );
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document.write( "solve for r to get:\r<BR>\n" );
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document.write( "r = 120\r<BR>\n" );
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document.write( "go back to the first original equation and replace r with 120 to get:\r<BR>\n" );
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document.write( "j/r = 3/5 becomes j/120 = 3/5\r<BR>\n" );
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document.write( "solve for j to get j = 120 * 3/5 = 24 * 3 = 72\r<BR>\n" );
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document.write( "you get j = 72 and r = 120; this is the same answer as before, just derived in a different way.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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