document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=719919>Question 719919</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When Butch and Kent left for their trip, the ratio of Butch's money to Kent's money was 7:3. After a short while Butch gave Kent $30, making the new ratio of their cash 3:2. When they started the trip how much more money did Butch have than Kent?\r<BR>\n" );
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document.write( "How to solve this problem the correct way?  I got the answer by process of elimination (just plugging in numbers till I found the correct answer) but I would like to know how to solve the problem the correct way.\r<BR>\n" );
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document.write( "For the first ratio 7:3, I found that Butch started with $210 and Kent with $90 (ratio 7:3)(7x30=210, 3x30=90). So Butch had $120 more than Kent when they started.\r<BR>\n" );
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document.write( "For the second ratio 3:2, if Butch gave Kent $30 he would have $180 (210-30=180) and Kent would have $120 (90+30=120) ending up with the correct 3:2 ratio. (3x60=180, 2x60=120).\r<BR>\n" );
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document.write( "But how can this be solved without just plugging in numbers until the correct answer is found? Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #441588 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=441588\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When Butch and Kent left for their trip, the ratio of Butch's money to Kent's money was 7:3.<BR>\n" );
document.write( " After a short while Butch gave Kent $30, making the new ratio of their cash 3:2. When they started the trip how much more money did Butch have than Kent?<BR>\n" );
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document.write( "Let x = the multiplier<BR>\n" );
document.write( "then<BR>\n" );
document.write( "7x = B's original amt<BR>\n" );
document.write( "and<BR>\n" );
document.write( "3x = K's amt<BR>\n" );
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document.write( "After a short while Butch gave Kent $30, making the new ratio of their cash 3:2. When they started the trip how much more money did Butch have than Kent?\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287x-30%29%2F%283x%2B30%29 ALIGN=MIDDLE  ALT=\"%287x-30%29%2F%283x%2B30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cross multiply<BR>\n" );
document.write( "2(7x-30) = 3(3x+30)<BR>\n" );
document.write( "14x - 60 = 9x + 90<BR>\n" );
document.write( "14x - 9x = 90 + 60<BR>\n" );
document.write( "5x = 150<BR>\n" );
document.write( "x = 30 is the multiplier<BR>\n" );
document.write( "then<BR>\n" );
document.write( "7(30) = $210 was B's amt<BR>\n" );
document.write( "3(30) = $90 was K's amt<BR>\n" );
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document.write( "differ: $120 amt B had more than K <BR>\n" );
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document.write( "You can confirm this, find the ratio of how much they had after the $30 exchange.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28210-30%29%2F%2890%2B30%29 ALIGN=MIDDLE  ALT=\"%28210-30%29%2F%2890%2B30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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