document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=983903>Question 983903</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi a and b had a total of 27 coins.when a gave 1/4 of his coins to b b had twice as many cojns as <BR>\n" );
document.write( "a .b then found out that she had twice as many 20cent coins as 10 cent coins.how much money<BR>\n" );
document.write( "did b have in the end.\r<BR>\n" );
document.write( "\n" );
document.write( "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 #604734 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=604734\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of coins a initially had.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of coins b initially had.<BR>\n" );
document.write( "You can find <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=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > by<BR>\n" );
document.write( "solving a system of equations, or by<BR>\n" );
document.write( "guess and check.<BR>\n" );
document.write( "From there, you can figure out how many coins b has in the end.<BR>\n" );
document.write( "Knowing how many coins b has in the end,<BR>\n" );
document.write( "and knowing that some of those coins are 10 cent coins,<BR>\n" );
document.write( "and the rest are 20 cent coins,<BR>\n" );
document.write( "with twice as many 20 cent coins as 10 cent coins,<BR>\n" );
document.write( "you can figure out how many coins of each kind b has in the end.<BR>\n" );
document.write( "Knowing how many coins of each kind b has in the end, you can figure out how much money those coins amount to.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "THE ALGEBRA WAY:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb=27 ALIGN=MIDDLE  ALT=\"a%2Bb=27\"   DISABLED_style= \"max-width:90%; height:auto;\" > because initially a and b had a total of 27 coins.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29a=0.25a ALIGN=MIDDLE  ALT=\"%281%2F4%29a=0.25a\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of coins a gave to b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-0.25a=0.75a ALIGN=MIDDLE  ALT=\"a-0.25a=0.75a\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of coins a had in the end.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.25a%2Bb ALIGN=MIDDLE  ALT=\"0.25a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of coins b had in the end.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%280.75a%29=0.25a%2Bb ALIGN=MIDDLE  ALT=\"2%280.75a%29=0.25a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > because in the end b had twice as many coins as <BR>\n" );
document.write( "a.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%280.75a%29=0.25a%2Bb ALIGN=MIDDLE  ALT=\"2%280.75a%29=0.25a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5a=0.25a%2Bb ALIGN=MIDDLE  ALT=\"1.5a=0.25a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5a-0.25a=b ALIGN=MIDDLE  ALT=\"1.5a-0.25a=b\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281.5-0.25%29a=b ALIGN=MIDDLE  ALT=\"%281.5-0.25%29a=b\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.25a=b ALIGN=MIDDLE  ALT=\"1.25a=b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%281.25a=b%2Ca%2Bb=27%29 ALIGN=MIDDLE  ALT=\"system%281.25a=b%2Ca%2Bb=27%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%281.25a=b%2Ca%2B1.25a=27%29 ALIGN=MIDDLE  ALT=\"system%281.25a=b%2Ca%2B1.25a=27%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%281.25a=b%2C2.25a=27%29 ALIGN=MIDDLE  ALT=\"system%281.25a=b%2C2.25a=27%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%281.25a=b%2Ca=27%2F2.25%29 ALIGN=MIDDLE  ALT=\"system%281.25a=b%2Ca=27%2F2.25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%281.25a=b%2Ca=12%29 ALIGN=MIDDLE  ALT=\"system%281.25a=b%2Ca=12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%281.25%2A12=b%2Ca=12%29 ALIGN=MIDDLE  ALT=\"system%281.25%2A12=b%2Ca=12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2815=b%2Ca=12%29 ALIGN=MIDDLE  ALT=\"system%2815=b%2Ca=12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.25a%2Bb=0.25%2A12%2A15=3%2B15=18 ALIGN=MIDDLE  ALT=\"0.25a%2Bb=0.25%2A12%2A15=3%2B15=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >= total number of coins b had in the end.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%7D%7D=+number+of+10+cent+coins+b+had+in+the+end.%0D%0A%7B%7B%7B2x%7D%7D=+number+of+20+cent+coins+b+had+in+the+end%2C%0D%0Abecause+in+the+end+b+had+twice+as+many+20+cent+coins+as+10+cent+coins.%0D%0A%7B%7B%7B2x%2Bx=3x=18 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >= total number of coins b had in the end.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=18 ALIGN=MIDDLE  ALT=\"3x=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=18%2F3 ALIGN=MIDDLE  ALT=\"x=18%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=2%2A6=12 ALIGN=MIDDLE  ALT=\"2x=2%2A6=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A%28%22%240.10%22%29=%22%240.60%22 ALIGN=MIDDLE  ALT=\"6%2A%28%22%240.10%22%29=%22%240.60%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > = value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > 10-cent coins.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2A%28%22%240.20%22%29=%22%242.40%22 ALIGN=MIDDLE  ALT=\"12%2A%28%22%240.20%22%29=%22%242.40%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > = value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > 20-cent coins.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%240.60%22%2B%22%242.40%22=highlight%28%22%243.00%22%29 ALIGN=MIDDLE  ALT=\"%22%240.60%22%2B%22%242.40%22=highlight%28%22%243.00%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= total value of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > 10-cent coins and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > 20-cent coins b had in the end.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "THE \"GUESS-AND-CHECK\" WAY:<BR>\n" );
document.write( "Since a and b initially had a total of 27 coins, and a gave 1/4 of his coins to b,<BR>\n" );
document.write( "initially a must have had a number of coins that divides by 4 evenly, and is less than 27,<BR>\n" );
document.write( "such as 4, or 8, or 12, or 16, or 20, or 24.<BR>\n" );
document.write( "If it was 4, b would have initially had 27-4=23 coins;<BR>\n" );
document.write( "a would have given b just 1 coin, keeping the other 4-1=3 coins,<BR>\n" );
document.write( "and b would have had 23+3=26 coins in the end.<BR>\n" );
document.write( "Those 26 coins are a much greater number of coins than twice the 3 coins a had in the end.<BR>\n" );
document.write( "So, b must have started with less than 23 coins and a must have started with more than 4 coins.<BR>\n" );
document.write( "If a started with 8 coins, a would have given 2 of them to b, ending with 8-2=6 coins,<BR>\n" );
document.write( "while b would have started with 27-8=19 coins, and would have ended with 19+2=21.<BR>\n" );
document.write( "Those 21 coins are a greater number of coins than twice the 6 coins a had in the end.<BR>\n" );
document.write( "So, a must have started with more than 8 coins.<BR>\n" );
document.write( "If a started with 12 coins, a would have given 3 of them to b, ending with 12-3=9 coins,<BR>\n" );
document.write( "while b would have started with 27-12=15 coins, and would have ended with 15+3=18,<BR>\n" );
document.write( "which is twice as many coins as the 9 coins a ended up with.<BR>\n" );
document.write( "So, a started with 12 coins, and b had 18 coins in the end.<BR>\n" );
document.write( "Those 21 coins are a greater number of coins than twice the 6 coins a had in the end.<BR>\n" );
document.write( "From there you can continue as above, or guess-and-check to find how many of those 18 coins are 10 cent coins.<BR>\n" );
document.write( "If at the end just 1 of the coins  b had was a 10-cent coin, b would have had 2 20-cent coins for a total of 1+2=3 coins.<BR>\n" );
document.write( "So the number of 10-cent coins must b had in the end must have been more than 1.<BR>\n" );
document.write( "If at the end just 5 of the coins b had were 10-cent coins, b would have had twice 5, or 10 20-cent coins for a total of 5+10=15 coins.<BR>\n" );
document.write( "Since b had 18 coins at the end, and 18 is more than 15,<BR>\n" );
document.write( "the number of 10-cent coins must b had in the end must have been more than 5.<BR>\n" );
document.write( "If at the end 6 of the coins b had were 10-cent coins, b would have had twice 6, or 12 20-cent coins for a total of 6+12=18 coins.<BR>\n" );
document.write( "Since b had 18 coins at the end, that is the mix of coins b had at the end,<BR>\n" );
document.write( "and 6 10-cent coins plus 12 20-cent coins make $3.00.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );