document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201235>Question 1201235</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "Bob and Jill had some sweets. After Jill gave Bob 20% of what she had Bob would have 60% more than Jill. What percentage of his total number of sweets must Bob give to Jill so that they will have the same number of sweets. <BR>\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835522 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=835522\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let b = the number of sweets that bob had.<BR>\n" );
document.write( "let j = the number of sweets that jill had.\r<BR>\n" );
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document.write( "After Jill gave Bob 20% of what she had, Bob would have 60% more than Jill. \r<BR>\n" );
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document.write( "assume jill had x number of sweets.<BR>\n" );
document.write( "after she gave 20% of them to bob, she would have had .8x number of sweets left.\r<BR>\n" );
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document.write( "after jill gave 20% of her sweets to bob, bob would have had 1.6 * the number of sweets that jill had left.\r<BR>\n" );
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document.write( "bob would have had 1.6 * .8 * x = 1.28 * x sweets.\r<BR>\n" );
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document.write( "after the transaction:<BR>\n" );
document.write( "bob had 1.28 * x number of sweets.<BR>\n" );
document.write( "jill had .8 * x number of sweets.\r<BR>\n" );
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document.write( "you want to know what percentage of sweets that bob had were given to jill so that they both have the same number of sweets.\r<BR>\n" );
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document.write( "let that quantity be equal to y.\r<BR>\n" );
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document.write( "you get 1.28 * x - y = .8 * x + y<BR>\n" );
document.write( "add y to both sides of this equation and subtract .8 * x from both sides of this equation to get:<BR>\n" );
document.write( "1.28 * x - .8 * x = 2 * y<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( ".48 * x = 2 * y<BR>\n" );
document.write( "solve for y to get:<BR>\n" );
document.write( "y = .48 / 2 = .24 * x\r<BR>\n" );
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document.write( "replace y with .24 * x in the equation of 1.28 * x - y = .8 * x + y.<BR>\n" );
document.write( "the equation becomes:<BR>\n" );
document.write( "1.28 * x - .24 * x = .8 * x + .24 * x<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "1.04 * x = 1.04 * x\r<BR>\n" );
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document.write( "the ratio of .24 * x to 1.28 * x is equal to (.24 * x) / (1.28 * x) = .1875.<BR>\n" );
document.write( "this suggest that bob would have had to give 18.75% of what he had to jill so that they would both have the same amount.\r<BR>\n" );
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document.write( "to see if this makes sense, let x = any random number that makes some kind of sense.<BR>\n" );
document.write( "i let x = 1000\r<BR>\n" );
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document.write( "that's the amount that jill had to start with.<BR>\n" );
document.write( "she gave 20% of that to bob<BR>\n" );
document.write( "bob would then have had 1.6 * what jill had left.<BR>\n" );
document.write( "jill would have had 800 left.<BR>\n" );
document.write( "bob would have had 1280, because 1.6 * 800 = 1280.\r<BR>\n" );
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document.write( "bob would then have had to give 18.75% of that to jill so that they would both have the same amount.<BR>\n" );
document.write( ".1875 * 1280 = 240.<BR>\n" );
document.write( "bob gave 240 to jill.<BR>\n" );
document.write( "bob now has 1280 - 240 = 1040.<BR>\n" );
document.write( "jill now has 800 + 240 = 1040.<BR>\n" );
document.write( "they both now have the same amount.\r<BR>\n" );
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document.write( "it looks like your solution is that bob would have had to give 18.75% of his sweets to jill so that they would both have the same number of sweets.\r<BR>\n" );
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