document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=12331>Question 12331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Aunt Alice gave each of her three nieces a number of silver dollars equal to their ages. The youngest felt that this was unfair. They agreed to redistribute the money. The youngest would split half of her silver dollars evenly with the other two sisters. The middle would then give each of the others 4 silver dollars. Finally, the oldest was to split half of her dollars equally between the two younger sisters. After exchanging the money, each girl had 16 silver dollars. How old are the sisters? (Their ages = 48)\r<BR>\n" );
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document.write( "MUST HAVE PROCESS </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #6262 by </B><A HREF=/tutors/aboutme.mpl?userid=bonster><B>bonster(299)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bonster><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=6262\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> youngest=x<BR>\n" );
document.write( "middle=y<BR>\n" );
document.write( "oldest=z\r<BR>\n" );
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document.write( "The youngest kept half and gave 1/4 each to her sisters<BR>\n" );
document.write( "x:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2 ALIGN=MIDDLE  ALT=\"x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y:Y+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "z:Z+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The middle gave the oldest and youngest 4 each<BR>\n" );
document.write( "x:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2 ALIGN=MIDDLE  ALT=\"x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >+4<BR>\n" );
document.write( "y:Y+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >-8<BR>\n" );
document.write( "z:Z+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >+4\r<BR>\n" );
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document.write( "the oldest kept half z so (Z+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >+4) becomes:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F2 ALIGN=MIDDLE  ALT=\"z%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F8 ALIGN=MIDDLE  ALT=\"x%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >+2<BR>\n" );
document.write( "she gives half of that to each sister so they receive:  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F4 ALIGN=MIDDLE  ALT=\"z%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F16 ALIGN=MIDDLE  ALT=\"x%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >+1)\r<BR>\n" );
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document.write( "x:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2 ALIGN=MIDDLE  ALT=\"x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >+4+(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F4 ALIGN=MIDDLE  ALT=\"z%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F16 ALIGN=MIDDLE  ALT=\"x%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >+1)=16<BR>\n" );
document.write( "y:Y+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >-8+(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F4 ALIGN=MIDDLE  ALT=\"z%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F16 ALIGN=MIDDLE  ALT=\"x%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >+1)=16<BR>\n" );
document.write( "z:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F2 ALIGN=MIDDLE  ALT=\"z%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F8 ALIGN=MIDDLE  ALT=\"x%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >+2=16\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2 ALIGN=MIDDLE  ALT=\"x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >+4+(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F4 ALIGN=MIDDLE  ALT=\"z%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F16 ALIGN=MIDDLE  ALT=\"x%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >+1)=16   <--subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2 ALIGN=MIDDLE  ALT=\"x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and 4 from both sides<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F4 ALIGN=MIDDLE  ALT=\"z%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F16 ALIGN=MIDDLE  ALT=\"x%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >+1)=16-4-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2 ALIGN=MIDDLE  ALT=\"x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F4 ALIGN=MIDDLE  ALT=\"z%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F16 ALIGN=MIDDLE  ALT=\"x%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >+1)=12-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2 ALIGN=MIDDLE  ALT=\"x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "y+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >-8+(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F4 ALIGN=MIDDLE  ALT=\"z%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F16 ALIGN=MIDDLE  ALT=\"x%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >+1)=16  <--subtract y and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and add 8 to both sides <BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F4 ALIGN=MIDDLE  ALT=\"z%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F16 ALIGN=MIDDLE  ALT=\"x%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >+1)=16+8-y-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F4 ALIGN=MIDDLE  ALT=\"z%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F16 ALIGN=MIDDLE  ALT=\"x%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >+1)=24-y-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "since 12-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2 ALIGN=MIDDLE  ALT=\"x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and 24-y-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  both equal (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F4 ALIGN=MIDDLE  ALT=\"z%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F16 ALIGN=MIDDLE  ALT=\"x%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >+1), you can equate them and solve for y:<BR>\n" );
document.write( "12-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2 ALIGN=MIDDLE  ALT=\"x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=24-y-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "12-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2F4 ALIGN=MIDDLE  ALT=\"2x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=24-y-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >   <--add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2F4 ALIGN=MIDDLE  ALT=\"2x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides<BR>\n" );
document.write( "12=24-y+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >     <--add y to both sides<BR>\n" );
document.write( "12+y=24+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >      <--subtract 12 from both sides<BR>\n" );
document.write( "y=12+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "to solve for z: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F2 ALIGN=MIDDLE  ALT=\"z%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F8 ALIGN=MIDDLE  ALT=\"x%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >+2=16  <--subtract 2 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F2 ALIGN=MIDDLE  ALT=\"z%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F8 ALIGN=MIDDLE  ALT=\"x%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >=14     <--subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F8 ALIGN=MIDDLE  ALT=\"x%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F2 ALIGN=MIDDLE  ALT=\"z%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=14-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F8 ALIGN=MIDDLE  ALT=\"x%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >    <--multiply both sides by 2<BR>\n" );
document.write( "z=28-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "plug it back to x+y+z=48<BR>\n" );
document.write( "x+(12+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >)+(28-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=48<BR>\n" );
document.write( "x+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >+12+28=48<BR>\n" );
document.write( "x+40=48<BR>\n" );
document.write( "x=8\r<BR>\n" );
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document.write( "since the youngest=x, she is 8 years old<BR>\n" );
document.write( "middle y=(12+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=12+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F4 ALIGN=MIDDLE  ALT=\"8%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=12+2=14<BR>\n" );
document.write( "oldest z=28-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=28-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F4 ALIGN=MIDDLE  ALT=\"8%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=28-2=26 \r<BR>\n" );
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document.write( "They are 8, 14, and 26 years old.<BR>\n" );
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