document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164470>Question 164470</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 12 silver dollars. How old are the sisters? (Their ages = 36)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121213 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=121213\">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=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >= youngest age<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >= middle one's age<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >= oldest one's age<BR>\n" );
document.write( "The youngest would split half of her silver dollars evenly with the other two sisters.<BR>\n" );
document.write( "The middle and oldest sisters get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F4 ALIGN=MIDDLE  ALT=\"a%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F4 ALIGN=MIDDLE  ALT=\"a%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > silver dollars<BR>\n" );
document.write( "The middle, who now has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+%2B+a%2F4 ALIGN=MIDDLE  ALT=\"b+%2B+a%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the others<BR>\n" );
document.write( "So, the middle now has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+%2B+a%2F4+-+8 ALIGN=MIDDLE  ALT=\"b+%2B+a%2F4+-+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The youngest has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F2+%2B+4 ALIGN=MIDDLE  ALT=\"a%2F2+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The oldest has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+%2B+a%2F4+%2B+4 ALIGN=MIDDLE  ALT=\"c+%2B+a%2F4+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now the oldest gives 1/2 her money to the other sisters<BR>\n" );
document.write( "The oldest now has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2F2+%2B+a%2F8+%2B+2 ALIGN=MIDDLE  ALT=\"c%2F2+%2B+a%2F8+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Each sister gets <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%2A%28c+%2B+a%2F4+%2B+4%29 ALIGN=MIDDLE  ALT=\"%281%2F4%29%2A%28c+%2B+a%2F4+%2B+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the middle one has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2F4+%2B+a%2F16+%2B+1+%2B+b+%2B+a%2F4+-+8 ALIGN=MIDDLE  ALT=\"c%2F4+%2B+a%2F16+%2B+1+%2B+b+%2B+a%2F4+-+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And, the youngest has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2F4+%2B+a%2F16+%2B+1+%2B+a%2F2+%2B+4 ALIGN=MIDDLE  ALT=\"c%2F4+%2B+a%2F16+%2B+1+%2B+a%2F2+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now each girl has 12 silver dollars<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2F4+%2B+a%2F16+%2B+1+%2B+a%2F2+%2B+4+=+12 ALIGN=MIDDLE  ALT=\"c%2F4+%2B+a%2F16+%2B+1+%2B+a%2F2+%2B+4+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9a%2F16+%2B+c%2F4+%2B+5+=+12 ALIGN=MIDDLE  ALT=\"9a%2F16+%2B+c%2F4+%2B+5+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > (youngest)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5a%2F16+%2B+b+%2B+c%2F4+-+7+=+12 ALIGN=MIDDLE  ALT=\"5a%2F16+%2B+b+%2B+c%2F4+-+7+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > middle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2F16+%2B+c%2F2+%2B+2+=+12 ALIGN=MIDDLE  ALT=\"2a%2F16+%2B+c%2F2+%2B+2+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > oldest<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "Multiply each equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9a+%2B+4c+%2B+80+=+12%2A16 ALIGN=MIDDLE  ALT=\"9a+%2B+4c+%2B+80+=+12%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5a+%2B+16b+%2B+4c+-+112+=+12%2A16 ALIGN=MIDDLE  ALT=\"5a+%2B+16b+%2B+4c+-+112+=+12%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a+%2B+8c+%2B+32+=+12%2A16 ALIGN=MIDDLE  ALT=\"2a+%2B+8c+%2B+32+=+12%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "Multiply (1) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then subtract (3) from (1)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18a+%2B+8c+%2B+160+=+2%2A12%2A16 ALIGN=MIDDLE  ALT=\"18a+%2B+8c+%2B+160+=+2%2A12%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2a+-+8c+-32+=+-12%2A16 ALIGN=MIDDLE  ALT=\"-2a+-+8c+-32+=+-12%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16a+%2B+128+=+12%2A16 ALIGN=MIDDLE  ALT=\"16a+%2B+128+=+12%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16a+=+192+-+128 ALIGN=MIDDLE  ALT=\"16a+=+192+-+128\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16a+=+64 ALIGN=MIDDLE  ALT=\"16a+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+4 ALIGN=MIDDLE  ALT=\"a+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute this in (3)<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A4+%2B+8c+%2B+32+=+192 ALIGN=MIDDLE  ALT=\"2%2A4+%2B+8c+%2B+32+=+192\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8c+=+192+-+40 ALIGN=MIDDLE  ALT=\"8c+=+192+-+40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8c+=+152 ALIGN=MIDDLE  ALT=\"8c+=+152\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+19 ALIGN=MIDDLE  ALT=\"c+=+19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > in (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A4+%2B+16b+%2B+4%2A19+-+112+=+192 ALIGN=MIDDLE  ALT=\"5%2A4+%2B+16b+%2B+4%2A19+-+112+=+192\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+%2B+16b+%2B+76+-+112+=+192 ALIGN=MIDDLE  ALT=\"20+%2B+16b+%2B+76+-+112+=+192\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16b+=+192+%2B+112+-+20+-+76 ALIGN=MIDDLE  ALT=\"16b+=+192+%2B+112+-+20+-+76\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16b+=+208 ALIGN=MIDDLE  ALT=\"16b+=+208\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+13 ALIGN=MIDDLE  ALT=\"b+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" >    <BR>\n" );
document.write( "Their ages are 4,13 and 19 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );