document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=890566>Question 890566</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mr Tong has some guavas and papayas in two crates. In crate A, the number of guavas and papayas are in the ratio  of 5:3. In crate B, the number of guavas is 4/9 the number of papayas. Mr Tong transfers half of the guavas from crate A to crate B. The number of fruits in crate A becomes 308 and the ratio of the number of guavas to the number of papayas in crate B becomes 5:6. \r<BR>\n" );
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document.write( "(a) How many guavas have been transferred from crate A to crate B?\r<BR>\n" );
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document.write( "(b) What is the number of fruits in crate B after the transfer? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #539078 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=539078\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = number of guavas in crate A<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%5BA%5D+ ALIGN=MIDDLE  ALT=\"+p%5BA%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of papayas in crate A<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BB%5D+ ALIGN=MIDDLE  ALT=\"+g%5BB%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = number of guavas in crate B<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%5BB%5D+ ALIGN=MIDDLE  ALT=\"+p%5BB%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of papayas in crate B<BR>\n" );
document.write( "----------------------------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D+%2F+p%5BA%5D+=+5%2F3+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D+%2F+p%5BA%5D+=+5%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BB%5D+=+%284%2F9%29%2Ap%5BB%5D+ ALIGN=MIDDLE  ALT=\"+g%5BB%5D+=+%284%2F9%29%2Ap%5BB%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BB%5D+%2F+p%5BB%5D+=+4%2F9+ ALIGN=MIDDLE  ALT=\"+g%5BB%5D+%2F+p%5BB%5D+=+4%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "After transfer:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D+%2F+2+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > guavas in crate A<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D+%2F+2+%2B+g%5BB%5D+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D+%2F+2+%2B+g%5BB%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > guavas in crate B<BR>\n" );
document.write( "------------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+308+ ALIGN=MIDDLE  ALT=\"+308+\"   DISABLED_style= \"max-width:90%; height:auto;\" > fruits in crate A<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D+%2F+2+%2B+p%5BA%5D+=+308+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D+%2F+2+%2B+p%5BA%5D+=+308+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+g%5BA%5D+%2F+2+%2B+g%5BB%5D+%29+%2F+p%5BB%5D+=+5%2F6+ ALIGN=MIDDLE  ALT=\"+%28+g%5BA%5D+%2F+2+%2B+g%5BB%5D+%29+%2F+p%5BB%5D+=+5%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D+%2F+2+%2B+p%5BA%5D+=+308+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D+%2F+2+%2B+p%5BA%5D+=+308+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, from (1):<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D+%2F+p%5BA%5D+=+5%2F3+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D+%2F+p%5BA%5D+=+5%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D+=+%285%2F3%29%2Ap%5BA%5D+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D+=+%285%2F3%29%2Ap%5BA%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%5BA%5D+=+%28+3%2F5+%29%2Ag%5BA%5D+ ALIGN=MIDDLE  ALT=\"+p%5BA%5D+=+%28+3%2F5+%29%2Ag%5BA%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By substitution:<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D+%2F+2+%2B+%28+3%2F5+%29%2Ag%5BA%5D+=+308+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D+%2F+2+%2B+%28+3%2F5+%29%2Ag%5BA%5D+=+308+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D+%2A%28+1%2F2+%2B+3%2F5+%29+=+308+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D+%2A%28+1%2F2+%2B+3%2F5+%29+=+308+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D%2A%28+11%2F10+%29+=+308+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D%2A%28+11%2F10+%29+=+308+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D+=+%28+10%2F11+%29%2A308+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D+=+%28+10%2F11+%29%2A308+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D+=+280+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D+=+280+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BB%5D+%2F+p%5BB%5D+=+4%2F9+ ALIGN=MIDDLE  ALT=\"+g%5BB%5D+%2F+p%5BB%5D+=+4%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%5BB%5D+=+%289%2F4%29%2Ag%5BB%5D+ ALIGN=MIDDLE  ALT=\"+p%5BB%5D+=+%289%2F4%29%2Ag%5BB%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And, after transfer:<BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28+g%5BA%5D+%2F+2+%2B+g%5BB%5D+%29%29+%2F+p%5BB%5D+=+5%2F6+ ALIGN=MIDDLE  ALT=\"+%28%28+g%5BA%5D+%2F+2+%2B+g%5BB%5D+%29%29+%2F+p%5BB%5D+=+5%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28+280+%2F+2+%2B+g%5BB%5D+%29%29+%2F+p%5BB%5D+=+5%2F6+ ALIGN=MIDDLE  ALT=\"+%28%28+280+%2F+2+%2B+g%5BB%5D+%29%29+%2F+p%5BB%5D+=+5%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28+140+%2B+g%5BB%5D+%29%29+%2F+p%5BB%5D+=+5%2F6+ ALIGN=MIDDLE  ALT=\"+%28%28+140+%2B+g%5BB%5D+%29%29+%2F+p%5BB%5D+=+5%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+140+%2B+g%5BB%5D+=+%285%2F6%29%2Ap%5BB%5D+ ALIGN=MIDDLE  ALT=\"+140+%2B+g%5BB%5D+=+%285%2F6%29%2Ap%5BB%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute (2) into (4)<BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+140+%2B+g%5BB%5D+=+%285%2F6%29%2A%289%2F4%29%2Ag%5BB%5D+ ALIGN=MIDDLE  ALT=\"+140+%2B+g%5BB%5D+=+%285%2F6%29%2A%289%2F4%29%2Ag%5BB%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+140+%2B+g%5BB%5D+=+%28+15%2F8+%29%2Ag%5BB%5D+ ALIGN=MIDDLE  ALT=\"+140+%2B+g%5BB%5D+=+%28+15%2F8+%29%2Ag%5BB%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+7%2F8+%29%2Ag%5BB%5D+=+140+ ALIGN=MIDDLE  ALT=\"+%28+7%2F8+%29%2Ag%5BB%5D+=+140+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BB%5D+=+%288%2F7%29%2A140+ ALIGN=MIDDLE  ALT=\"+g%5BB%5D+=+%288%2F7%29%2A140+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BB%5D+=+160+ ALIGN=MIDDLE  ALT=\"+g%5BB%5D+=+160+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D+%2F+2+=+280%2F2+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D+%2F+2+=+280%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D+%2F+2+=+140+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D+%2F+2+=+140+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "(a) 140 guavas were transferred to crate B<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+g%5BA%5D+%2F+2+%2B+g%5BB%5D+%29+%2F+p%5BB%5D+=+5%2F6+ ALIGN=MIDDLE  ALT=\"+%28+g%5BA%5D+%2F+2+%2B+g%5BB%5D+%29+%2F+p%5BB%5D+=+5%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+280+%2F+2+%2B+160+%29+%2F+p%5BB%5D+=+5%2F6+ ALIGN=MIDDLE  ALT=\"+%28+280+%2F+2+%2B+160+%29+%2F+p%5BB%5D+=+5%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+140+%2B+160+%29+%2F+p%5BB%5D+=+5%2F6+ ALIGN=MIDDLE  ALT=\"+%28+140+%2B+160+%29+%2F+p%5BB%5D+=+5%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%5BB%5D+=+300%2A%28+6%2F5+%29+ ALIGN=MIDDLE  ALT=\"+p%5BB%5D+=+300%2A%28+6%2F5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%5BB%5D+=+360+ ALIGN=MIDDLE  ALT=\"+p%5BB%5D+=+360+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "After the transfer, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D+%2F+2+%2B+g%5BB%5D+%2B+p%5BB%5D+=+140+%2B+160+%2B+360+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D+%2F+2+%2B+g%5BB%5D+%2B+p%5BB%5D+=+140+%2B+160+%2B+360+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D+%2F+2+%2B+g%5BB%5D+%2B+p%5BB%5D+=+660+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D+%2F+2+%2B+g%5BB%5D+%2B+p%5BB%5D+=+660+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "(b) There are 660 fruits in crate B<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D+%2F+p%5BA%5D+=+5%2F3+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D+%2F+p%5BA%5D+=+5%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%5BA%5D+=+%283%2F5%29%2Ag%5BA%5D+ ALIGN=MIDDLE  ALT=\"+p%5BA%5D+=+%283%2F5%29%2Ag%5BA%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%5BA%5D+=+%283%2F5%29%2A280+ ALIGN=MIDDLE  ALT=\"+p%5BA%5D+=+%283%2F5%29%2A280+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%5BA%5D+=+168+ ALIGN=MIDDLE  ALT=\"+p%5BA%5D+=+168+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%5BA%5D+%2F+2+%2B+p%5BA%5D+=+308+ ALIGN=MIDDLE  ALT=\"+g%5BA%5D+%2F+2+%2B+p%5BA%5D+=+308+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+140+%2B+168+=+308+ ALIGN=MIDDLE  ALT=\"+140+%2B+168+=+308+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+308+=+308+ ALIGN=MIDDLE  ALT=\"+308+=+308+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );