document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197783>Question 1197783</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jake, Mandy and Ann had 360 sweets in the ratio 4:3:5 respectively. Jake gave 1/3 of his sweet to Mandy and Ann gave 40% of her sweets to Jake. What was the ratio of Jake's sweet to Ann's sweets in the end? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831185 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=831185\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The ratio 4:3:5 scales up to 4x:3x:5x for some positive whole number x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Jake has 4x pieces, Mandy has 3x, and Ann has 5x.<BR>\n" );
document.write( "Their counts total to 360.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4x+3x+5x = 360<BR>\n" );
document.write( "12x = 360<BR>\n" );
document.write( "x = 360/12<BR>\n" );
document.write( "x = 30\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then we can find the following:<BR>\n" );
document.write( "Jake = 4x = 4*30 = 120 <BR>\n" );
document.write( "Mandy = 3x = 3*30 = 90 <BR>\n" );
document.write( "Ann = 5x = 5*30 = 150\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Check so far:<BR>\n" );
document.write( "jake + mandy + ann = 120+90+150 = 210+150 = 360<BR>\n" );
document.write( "This confirms we did things correctly.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Jake has 120 sweets<BR>\n" );
document.write( "He gives 1/3 of it to Mandy<BR>\n" );
document.write( "1/3 of 120 = (1/3)*120 = 40<BR>\n" );
document.write( "He gives 40 pieces to Mandy\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Jake: 120 to 120-40 = 80<BR>\n" );
document.write( "Mandy: 90 to 90+40 = 130\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Ann has 150 pieces. She gives 40% to Jake.<BR>\n" );
document.write( "40% of 150 = 0.40*150 = 60<BR>\n" );
document.write( "She gives him 60 pieces.<BR>\n" );
document.write( "Jake: 80+60 = 140<BR>\n" );
document.write( "Ann: 150-60 = 90\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We have these counts at this point <BR>\n" );
document.write( "Jake = 140<BR>\n" );
document.write( "Mandy = 130<BR>\n" );
document.write( "Ann = 90 <BR>\n" );
document.write( "Add those three values up and you should get 360 as a checksum. <BR>\n" );
document.write( "We haven't introduced new pieces of candy, nor taken away any from the entire group. All that has been done is the candy is shifted around.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The ratio of Jake's candy count to Ann's count is<BR>\n" );
document.write( "Jake: Ann<BR>\n" );
document.write( "140:90<BR>\n" );
document.write( "14:9<BR>\n" );
document.write( "I divided both parts by the GCF 10 to reduce the ratio\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<font color=red>Answer is 14:9</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Edit: The tutor @josgarithmetic has made a typo in simplifying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-%281%2F3%29%284x%29%2B0.4%2A5x ALIGN=MIDDLE  ALT=\"4x-%281%2F3%29%284x%29%2B0.4%2A5x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The simplified result is NOT <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x%2F3 ALIGN=MIDDLE  ALT=\"20x%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Instead, it should be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14x%2F3 ALIGN=MIDDLE  ALT=\"14x%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "</font>\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );