document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204999>Question 1204999</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "Ali and baby have some great sweets. If ali gives baba 3/8 of his sweets the ratio of ali to babas sweets is 1 to 2. What is the ratio of ali to babas sweets at first. <BR>\n" );
document.write( "Thanks <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 #841585 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841585\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Normally we go from \"before\" to \"after\", but I'll go in reverse.<BR>\n" );
document.write( "Ali ends with 'a' number of candies and Baba ends with twice as much 2a.<BR>\n" );
document.write( "This forms the ratio a:2a and that simplifies to 1:2 aka \"1 to 2\".\r<BR>\n" );
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document.write( "Then let b represent the amount Ali gifted to Baba.<BR>\n" );
document.write( "Ali would start with a+b candies<BR>\n" );
document.write( "Baba starts with 2a-b\r<BR>\n" );
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document.write( "After: ali = a, baba = 2a<BR>\n" );
document.write( "Before: ali = a+b, baba = 2a-b\r<BR>\n" );
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document.write( "Since b is the amount Ali gives to Baba, it is equal to 3/8 of the amount Ali had before giving their sweets.\r<BR>\n" );
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document.write( "b = (3/8)(a+b)<BR>\n" );
document.write( "8b = 3(a+b)<BR>\n" );
document.write( "8b = 3a+3b<BR>\n" );
document.write( "8b-3b = 3a<BR>\n" );
document.write( "5b = 3a<BR>\n" );
document.write( "b = 3a/5<BR>\n" );
document.write( "b = 0.6a\r<BR>\n" );
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document.write( "Then we find the ratio of their old amounts (a+b) over (2a-b)<BR>\n" );
document.write( "Plug in b = 0.6a found just now.<BR>\n" );
document.write( "(a+b)/(2a-b)<BR>\n" );
document.write( "= (a+0.6a)/(2a-0.6a)<BR>\n" );
document.write( "= (1.6a)/(1.4a)<BR>\n" );
document.write( "= (1.6)/(1.4)<BR>\n" );
document.write( "= 16/14<BR>\n" );
document.write( "= 8/7\r<BR>\n" );
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document.write( "In short,<BR>\n" );
document.write( "(a+b)/(2a-b) = 8/7<BR>\n" );
document.write( "when b = 0.6a\r<BR>\n" );
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document.write( "The fraction 8/7 leads to the ratio <font color=red>8:7</font> aka <font color=red>8 to 7</font><BR>\n" );
document.write( "It means that for every 8 pieces of candy Ali started with, Baba has 7 pieces to start with.\r<BR>\n" );
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document.write( "Let's say hypothetically Ali started with 8 pieces of candy.<BR>\n" );
document.write( "3/8 of that is 3 pieces, which is given to Baba.<BR>\n" );
document.write( "Ali's amount drops to 8-3 = 5 pieces<BR>\n" );
document.write( "Baba's amount increases to 7+3 = 10 pieces<BR>\n" );
document.write( "Their new ratio is 5:10 which reduces to 1:2<BR>\n" );
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