document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132011>Question 132011</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I keep a jar on my dresser for collecting the coins I find when I empty my pockets. This morning I counted my coins and found out the following:<BR>\n" );
document.write( "        One-fifth of the coins in my jar are dimes.<BR>\n" );
document.write( "        One-sixth of them are nickels.<BR>\n" );
document.write( "        One-tenth are quarters<BR>\n" );
document.write( "        The rest are pennies.<BR>\n" );
document.write( "The total value is $3.52.\r<BR>\n" );
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document.write( "How many of each coin do I have? \r<BR>\n" );
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document.write( "Tell how you got your answer and how you know it is correct.\r<BR>\n" );
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document.write( "Extra: I went to the bank and got coin wrappers. It takes $10 worth of quarters to fill a quarter wrapper, $5 worth of dimes to fill a dime wrapper, $2 worth of nickels to fill a nickel wrapper, and $0.50 worth of pennies to fill a penny wrapper.\r<BR>\n" );
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document.write( "How many more of each coin do I need before I can fill one wrapper of each? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #96499 by </B><A HREF=/tutors/aboutme.mpl?userid=harecurtis><B>harecurtis(6)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=harecurtis><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=96499\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=total number of coins in the jar<BR>\n" );
document.write( "(1/5)x are dimes valued at 0.10*(1/5)x dollars<BR>\n" );
document.write( "(1/6)x are nickels valued at 0.05(1/6)x dollars<BR>\n" );
document.write( "(1/10)x are quarters valued at 0.25*(1/10)x<BR>\n" );
document.write( "Now lets find out how many pennies before we go further. We can do that two ways:<BR>\n" );
document.write( "1. We can find out the value of the dimes, nickels and quarters and subtract that from $3.52, or:<BR>\n" );
document.write( "2. We can just find out what fractional part of (x) is left. Lets do #2:<BR>\n" );
document.write( "1/5+1/6 + 1/10 LCM is 30, so:<BR>\n" );
document.write( "(6/30)x+(5/30)x+(3/30)x=(14/30)x=dimes, nickels & quarters<BR>\n" );
document.write( "So 30/30-14/30=16/30=8/15x number of pennies<BR>\n" );
document.write( "Now we know that (8/15)x=number of pennies and 0.01*(8/15)x= value of pennies<BR>\n" );
document.write( "We are told that:<BR>\n" );
document.write( "0.10(1/5)x + 0.05(1/6)x+0.25(1/10x)+0.01(8/15)x=$3.52<BR>\n" );
document.write( "30 is still LCM so lets multiply each term by 30 to get rid of fractions:<BR>\n" );
document.write( "0.6x +0.25x+0.75x+0.16x=105.6 ($ are understood) collect like terms<BR>\n" );
document.write( "1.76x=105.6 divide both sides by 1.76<BR>\n" );
document.write( "x=60 ------------------------total number of coins in the jar\r<BR>\n" );
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document.write( "(1/5)x=(1/5)*60=12--------------------number of dimes<BR>\n" );
document.write( "(1/6)x=(1/6)*60=10---------------------number of nickels<BR>\n" );
document.write( "(1/10)x=(1/10)*60=6---------------------number of quarters<BR>\n" );
document.write( "(8/15)x=(8/15)*60=32----------------------number of pennies<BR>\n" );
document.write( "CK<BR>\n" );
document.write( "12+10+6+32=60<BR>\n" );
document.write( "60=60<BR>\n" );
document.write( "also<BR>\n" );
document.write( "0.10*12+0.05*10+0.25*6+0.01*32=$3.52<BR>\n" );
document.write( "$1.20+$0.50+$1.50+$0.32=$3.52<BR>\n" );
document.write( "$3.52=$3.52<BR>\n" );
document.write( "Extra: I went to the bank and got coin wrappers. It takes $10 worth of quarters to fill a quarter wrapper, $5 worth of dimes to fill a dime wrapper, $2 worth of nickels to fill a nickel wrapper, and $0.50 worth of pennies to fill a penny wrapper.<BR>\n" );
document.write( "How many more of each coin do I need before I can fill one wrapper of each?<BR>\n" );
document.write( "Quarters<BR>\n" );
document.write( "Have 6 for $1.50 Need 34 for 34*0.25 or $8.50<BR>\n" );
document.write( "Dimes<BR>\n" );
document.write( "Have 12 for $1.20 Need 38 for 38*0.10 or $3.80<BR>\n" );
document.write( "Nickels<BR>\n" );
document.write( "Have 10 for $0.50 Need 30 for 30*0.05 or $1.50<BR>\n" );
document.write( "Pennies<BR>\n" );
document.write( "Have 32 for $0.32 Need 68 for 68*0.01 or $0.68\r<BR>\n" );
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document.write( "Hope this helps </SPAN>\n" );
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