document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=596839>Question 596839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a coin bank contains $3.60 in half dollars and dimes. if there are 24 coins in all, how many of each type are there? what are the equations for this problem? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #377961 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=377961\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi there--<BR>\n" );
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document.write( "[I] Define your variables<BR>\n" );
document.write( "Let's have h be the number of half-dollars in the coin bank.<BR>\n" );
document.write( "Let's have d be the number of dimes in the coin bank.\r<BR>\n" );
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document.write( "The value of the half-dollars is $.50 times the number of half-dollars there are in the bank. One half-dollar is 0.50, two half-dollars are 2*(0.50)=$1.00, three are 3*(0.50)=$1.50. The algebraic expression is 0.50*h. <BR>\n" );
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document.write( "Using similar reasoning, the value of the dimes in the bank is 0.10*d since one dime is $0.10.<BR>\n" );
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document.write( "Set-up your equations:<BR>\n" );
document.write( "First make an equation for the total number of coins. There are 24 coins in all, so<BR>\n" );
document.write( "[the number of half-dollars] + [the number of dimes] = 24<BR>\n" );
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document.write( "In algebra, we write,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2Bd=24 ALIGN=MIDDLE  ALT=\"h%2Bd=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we will make an equation for the total value of the coins in the bank, $3.60.<BR>\n" );
document.write( "[the value of the half-dollars]  +  [the value of the dimes]  = $3.60<BR>\n" );
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document.write( "In algebra, we write,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.50h%2B0.10%2Ad=3.60 ALIGN=MIDDLE  ALT=\"0.50h%2B0.10%2Ad=3.60\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "[III] Solve the system of equations<BR>\n" );
document.write( "I will use the substitution method. Write the first equation in terms of d.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2Bd=24 ALIGN=MIDDLE  ALT=\"h%2Bd=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=24-h ALIGN=MIDDLE  ALT=\"d=24-h\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute 24-h for d in the second equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.50h%2B0.10d=3.60 ALIGN=MIDDLE  ALT=\"0.50h%2B0.10d=3.60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.50h%2B0.10%2824-h%29=3.60 ALIGN=MIDDLE  ALT=\"0.50h%2B0.10%2824-h%29=3.60\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now clear the parentheses.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.50h%2B2.40-0.10h=3.60 ALIGN=MIDDLE  ALT=\"0.50h%2B2.40-0.10h=3.60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine like terms.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.40h%2B2.40=3.60 ALIGN=MIDDLE  ALT=\"0.40h%2B2.40=3.60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 2.40 from both sides of the equation to isolate the h-term and the constant term on opposite sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.40h=1.20 ALIGN=MIDDLE  ALT=\"0.40h=1.20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides of the equation by 0.40 to isolate h.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3 ALIGN=MIDDLE  ALT=\"h=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The equation h=3 means that there are 3 half-dollars. Since there are 24 coins all together, there must be 21 dimes.<BR>\n" );
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document.write( "We need to make sure these coins have a total value of $3.60. Three half-dollars is $1.50, and twenty-one dimes is $2.10. $1.50+2.10=$3.60. BINGO!<BR>\n" );
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document.write( "That's it. Feel free to email me via gmail if any part of this explanation is unclear.<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com<BR>\n" );
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