document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185563>Question 1185563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tevin has a change jar that contains only pennies and dimes. He has 60 coins which add up to a total of $3.57. How many of each type of coin does he have?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816391 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=816391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The fastest way to find the answer is by logical reasoning with some simple mental arithmetic.<br><BR>\n" );
document.write( "With a total value of #3.57, the number of pennies must be one of these numbers:<br><BR>\n" );
document.write( "2, 7, 12, 17, ...<br><BR>\n" );
document.write( "So try one of those and see if it works; then adjust if needed.<br><BR>\n" );
document.write( "17 pennies would mean 60-17=43 dimes; $0.17+$4.30 = $4.47.  Too much.<br><BR>\n" );
document.write( "Maybe next try 37 pennies and 23 dimes: $2.30+$0.37 = $2.67.  Too little.<br><BR>\n" );
document.write( "Looking at those results and doing some easy calculations shows the correct total is exactly halfway between our two guesses.<br><BR>\n" );
document.write( "So try 27 pennies and 33 dimes. $3.30+$0.27 = $3.57.  Just right.<br><BR>\n" );
document.write( "ANSWER: 33 dimes and 27 pennies<br><BR>\n" );
document.write( "And here is another path that can teach you a good problem solving strategy when you are using guess-and-check.<br><BR>\n" );
document.write( "After finding that 17 pennies and 43 dimes was $4.47, which is $0.90 too much, you can logically reason that exchanging a dime for a penny reduces the total value by $0.09.  So to reduce the total $4.47 by $0.90 to get the correct total of $3.57, you need to exchange 10 dimes for pennies.<br><BR>\n" );
document.write( "So the correct combination is 43-10=33 dimes and 17+10=27 pennies.<br><BR>\n" );
document.write( "But probably a formal algebraic solution is wanted....<br><BR>\n" );
document.write( "x = # of dimes<BR>\n" );
document.write( "60-x = # of pennies<br><BR>\n" );
document.write( "The total value is $3.57 = 357 cents<br><BR>\n" );
document.write( "10x+1(60-x)=357<BR>\n" );
document.write( "10x+60-x=357<BR>\n" );
document.write( "9x=297<BR>\n" );
document.write( "x=33<br><BR>\n" );
document.write( "ANSWER: x=33 dimes, 60-x=27 pennies<br><BR>\n" );
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